How to use the Casio fx-115MS S-V.P.A.M. calculator

Click on any key to find out what it does.

A user guide for Math 099 students.   This site is best viewed with Mozilla Firefox at 800 x 600 or higher screen resolution.

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• Introduction:  to my Math 099 students  
  • The fx-115MS calculator
  •  About this guide  
  •  Calculator States  
  •  Self test  for checking screen pixels
• What the fx-115MS can do - Switching  MODES  
  •  Computation  
    •  Evaluate expressions ** 
    •  Solve Equations ** 
    •  Differentiation  
    •  Integration  
  •  Imaginary and Complex Numbers ** 
  •  Standard Deviation   and other single-variable statistical calculations
  •  Regression   Paired-variable statistical calculations
  •  Binary, Octal, Decimal, and Hexadecimal   calculations in other number systems
  •  Simultaneous Linear Equations **  Finding common solutions
  • Polynomial Equations **  Solving and Factoring
• How it  displays  information
  •  angles   Choices are: Degrees, Radians, or Gradians.
  •  numbers   Choices are: Fix, Sci, or Norm.
  •  Engineering  units: Femto, Pico, Nano, Micro, Milli, Kilo, Mega, Giga, or Tera.
  •  Complex number   coordinate system: Rectangular (a + bi) or Polar (r∠θ)
  •  Fractions **  Choices: Proper (Numerator < Denominator), or Improper (or vulgar).
  •  Decimal fractions   Separator symbol: Commas, or Dots (Periods)
• Return to Home Page

 ** These operations are used in Math 099.

To my Math 099 students

Overview of Math 099
Math 099 is intermediate algebra with geometry. It presupposes that you already know how to add, subtract, multiply, divide, raise to powers and extract roots using real numbers and fractions. Chapter one reviews the steps for solving equations with one variable and no powers (linear equations in one unknown). The rest of the book talks about graphing equations with two unknowns, solving simultaneous linear equations, rational expressions, complex numbers, radicals, and the "pièce de résistance", the "Grand Finale", the Big Boom when we set off all the remaining fireworks, which is the quadratic formula for solving second order equations in one unknown. All of this is done with an accompaniment of geometry examples in the background.
Another concept that is important in Mathematics is the inverse of a function. This would be the function that does the opposite of some other function. It can be used to undo what the other function did. For example if your function adds 5 to a number, the inverse function would be to subtract 5. If the original function multiplied by 12 then the inverse would divide by 12 or, equivalently, multiply by the reciprocal of 12. In this course we use the concept of the inverse function in chapter one as well as when we talk about radicals and powers being inverse functions.

My Grading Policy
I do not grade effort, I do not give extra points for good behavior, I do not give a minimum grade for perfect attendance. Worse yet, I do not give extra points for doing your homework, nor do I give partial credit for answers that are almost right. I only care about whether you can do math and get the right answer. Your answers are either right or they are wrong. Period. Either the Mars Lander is on target or it isn't. Either the patient gets the right medicine or he doesn't. If the lander misses the target, it is lost. If the patient is given the wrong amount of medicine he may die. I hope you understand how critical it can be for you to get the right answer. When you add ½ + ¾ I want you to be right every time.

Using calculators
There are so many new things to learn we really don't have time to work on the stuff you are supposed to already know. Some teachers may shrug and say there's nothing they can do about "your problem" and others may take time out from what they are supposed to be teaching and review remedial concepts. I really want to help you pass this course, but I want you to do it on my terms; you need to be able to get the right answers on my tests. I am so hung up on getting right answers that I will even allow you to use calculators. Because every calculator seems to work differently, you should never try using a calculator on a test until you have had a chance to do every problem with it. There are several calculators you might want to try but I am currently very positive on the Casio fx-115MS. It does fractions and complex numbers although it doesn't do radicals. I strongly encourage you to use it or another calculator that has the same fuctionality. In fact, even if you don't think you need a calculator, I strongly encourage you to use one to check your answers. This way you should be able to concentrate on understanding WHY you are doing the math instead of getting hung up on HOW to do it.

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About this user guide

Notation
I use curly braces { } when referring to keys that you press and brackets with [ bold text ] to show the answer.
For example, to add 2 plus 3 Press: {  2  }   {  +  }   {  3  }   {  =  }   [ 5 ]
I hope it doesn't confuse you but sometimes I got lazy and combined several keystrokes into one curly bracket, like this: {  2+3=  }   [ 5 ] Combining key strokes into a single reference reminds me of a horrible story about some people who die in an emergency when they couldn't dial nine-eleven because they couldn't find the eleven key on their cell phone. I hope I haven't caused you any similar distress.

The {  Hot Pink links  } are there to help you find the keys on your calculator or to tell you more about each key.

Browsers
Web pages are rendered differently by different browsers. Firefox and Netscape seem to do a better job of displaying the HTML special characters; however, even if you are using MS-InternetExplorer, if you look at my  Keyboard layout  and compare it to your calculator you should be able to figure out which symbol I am using for each key. If you find anything to be confusing, please let me know sooner rather than later.

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The fx-115MS is called the fx-912MS in Japan. It is a general purpose scientific calculator that has approximately 300 built-in functions but no graphing capabilities. It has a two line display and some deceptively sophisticated programmability. The top line is where you put your input, the bottom line is where the calculator displays its answers. The only tricky part to using the calculator is the funny looking circle labeled "copy" and "replay". This button also has four cursor controls for up, down, left and right.

Other keys can be used for various operations depending on the state of the calculator. The state can be set by using the  SHIFT and ALPHA  keys or by putting the calculator into certain   MODES  . You can tell the state of the calculator by looking at the little indicators above the first line of the display. Here is how to access the color coded functions associated with each key.

Color	How to get it
Black	Normal
RED	{  ALPHA  }
Brown	{  SHIFT  }
BLUE	SD or REG MODE
GREEN	BASE MODE

Different Calculator Logic Types. Calculators can be radically different in the way they operate. They use different keystroke sequences to enter the same formula. Do not make the mistake of borrowing someone else's calculator for a test unless you have been using it all along to do your homework. Here is a summary of various logic types that I saw at www.rskey.org .

Arithmetic. This logic type is typically associated with desk-top adding-machine type calculators. It's fine for accountants and bookkeepers, don't even think of using them in a Math or Science course.

Simple Algebraic. This is the algebraic logic used on most so-called four-function calculators. Calculators using this logic method will have an equal key but no parentheses keys. Slightly better than an arithmetic calculator but not really.

RPN stands for Reverse Polish Notation. RPN is characterized by an "Enter" key, and the absence of equals or parentheses keys. Hewlett-Packard has marketed RPN calculators for nearly 30 years. Today they still offer several RPN calculators, including a few dual mode RPN-algebraic calculators. RPN calculators are relatively expensive, with the cheapest going for around $60. They can do anything but they require you to totally rethink your formula before you enter it into the calculator.

Traditional Algebraic. This is the algebraic logic type used on many electronic calculators since the '70s. This logic type utilizes parentheses and an equal key. Unary operations (e.g. square root) are performed on a number already existing in the calculator's display register. Texas Instruments refers to their version of the traditional algebraic logic by the trademarked name AOS (Algebraic Operating System).

Formula Algebraic. This logic type is referred to by various trademarks: Casio's V.P.A.M. (Visually Perfect Algebraic Method), Sharp's D.A.L. (Direct Algebraic Logic), and Texas Instruments' EOS (Equation Operating System). It allows expressions to be entered in the same way as a mathematician would write them in an equation. For example, square root is entered before the expression on which it operates while square is entered after the expression. It is different from traditional algebraic calculators like Texas Instruments' AOS which use parentheses and an equal key but all unary operations are performed on the number in the calculator's display register.

S-V.P.A.M. stands for Super Visually Perfect Algebraic Method. This is the algebraic logic used on your fx-115MS. It is VPAM enhanced with a two line screen that lets you see your input together with the result. The calculator keeps a history of previous calculations which you can recall with the Replay feature, make any changes that you want, and then recalculate.

I have found instructions for the calculator in a PDF file on the CASIO web site here .

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CASIO   fx-115ms S-V.P.A.M. TWO WAY POWER FIRST LINE OF DISPLAY: expressions, formulas, and prompts SECOND LINE: answers   SHIFT     ALPHA     ↑     COPY     ←            →     REPLAY     ↓       MODE   CLR     ON     SOLVE   =     CALC     d/dx   :     ∫dx     x!     LOGIC     x-1     ³√     x³     d/c     a b/c     √     DEC     x²     x√     HEX     ^     10x   BIN     log     ex   OCT     e     ln    ⌈ ∠ ⌉  A     (-)     ←   B     ° ’ ”     C     hyp     sin-1   D     sin     cos-1   E     cos     tan-1   F     tan     STO     RCL     ←   i     ENG     (   ⌊ arg ⌋   X     )   ⌊ Abs ⌋   ;   Y     ,   ⌊ Conjg ⌋   M-   M     M+     DT  ⌊ CL ⌋   M     7     G     8     T     9     INS     DEL     OFF     AC     μ     4     m     5     k     6     nPr     ×     nCr     ÷   ⌈ S-SUM ⌉  f   1   ⌈ S-VAR ⌉  p 2 ⌈ DISTR ⌉  n   3   ⌈» r∠θ ⌉  Pol(   +   ⌈» a+bi ⌉  Rec(   -     Rnd     0     Ran#     •     π     EXP     DRG »     Ans   ⌈ Re⇔Im ⌉  %   =

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Addtional indicators on the screen are:

Up arrow	↑	There are prior screens in   Replay   memory
Down arrow	↓	There are subsequent screens in   Replay   memory
Right Arrow	→	there are additional menu choices you can get with the {  →  } key
Exponent   Base	×1088 d H b o	Used in Scientific Mode to indicate the exponent of 10 This same indicator is used in  Base  mode to indicate whether the displayed units are: d-Decimal, H-hexadecimal, b-Binary, o-octal and to execute   GREEN functions. .
Multi-Statement Mode	Disp	Indicates that the calculator is executing a Multi-statement command. Special thanks to Adam Sundor for telling me what this does.
Imaginary	i	The imaginary component of a  Complex number  number in a+bi form.
Angle	∠	The angle argument of a  Complex number  number in r∠θ form
Left Arrow	←	there are additional menu choices you can get with the {  ←  } key

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How to test all pixels on the screen.

Each digit on the second line is made up of 7 line segments. If any of them cease to operate correctly you could be misreading the data and putting the wrong answers on your homework and tests. I think it is important to check your display from time to time. To do this, follow these instructions.

Press and Hold {  SHIFT  }
Press and Hold {  7  }
Press {  ON  }
Release all three keys.
Press {  SHIFT  } 15 times to cycle through test screens. Here is what the first screen looks like. The second screen is totally blank. Screens 5-14 display the digits 0-9 all the way across the second line. Screens 15 & 16 contain just one digit 0 and 1.
Pressing {  ALPHA  } after the end of the test displays a 2. (Because it is the second key on the keyboard? Why don't the other keys seem to do anything?)

Press {  ON  } any time to exit the test.

I've been told that on earlier versions of the fx-115MS you only need to press the {  SHIFT  } and {  ON  } keys without the {  7  } key. Of course you don't want to be doing this if you are in the middle of a calculation since this will clear things out.

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The {  SHIFT  } and {  ALPHA  } state keys

These two keys change the   state   of the keyboard and determine what other keys on the calculator will do.

When you press the {  SHIFT  } key a white on black icon with the letter [S] appears on line 1 of the display window and the calculator enters the [S] state. When you press the {  ALPHA  } key the letter [A] appears and the [A] state is entered.

When the calculator is in the [S] state, pressing any key that has a BROWN inscription will invoke the corresponding function. In the [A] state the RED functions are executed.

Pressing any key will cause a state to be cleared whether or not there is a function associated with that state and key combination.

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The {  ↑  } (up arrow) key

This key is used all over the place to review input data as well as to scroll through output results.

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The {  SHIFT  }   {  COPY  } key

The Copy Key allows you to several combine lines from {  Replay  } memory into a {  multi-statement.  } What you need to do is to use the up arrow key to go back to a previous expression in Replay Memory. Pressing {  SHIFT  } {  COPY  } will combine all the expressions starting from that line and going forward into a multi-statement.

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The {  ←  } (left arrow) key

This key is used when editing the top line of the display as well as in switching between alternate sets of menus. You can tell if there are additional menu choices by checking the → or the ←   state   indicators.

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The {  →  } (right arrow) key

This key is used when editing the top line of the display as well as in switching between alternate sets of menus. You can tell if there are additional menu choices by checking the → or the ←   state   indicators.

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The {  REPLAY  } key

The replay key allows you to call up SOME previous calculations, optionally change them, and recalculate them. I say SOME previous calculations since there seem to be a lot of situations which clear out the replay memory. If there is anything in replay memory you should see the either the ↑ or ↓   state   indicators turned on. You can scroll through the replay memory by using the {  ↑  } and {  ↓  } keys.

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The {  ↓  } (down arrow) key

This key is used all over the place to review input data as well as to scroll through output results.

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The {  MODE  } Key.

The Mode key allows you to switch between different calculator modes and to change settings having to do with how information is displayed.

Press the {  MODE  } Key repeatedly until you get to the desired menu and then press the key associated with your selection. Click  here  to see a list of modes and settings.

1.  MODE  key submenu: 1-COMP   2-CMPLX
   1. Press {  1  } to select Computational Mode for all normal scientific calculator functions. BLUE and GREEN keys having to do with Complex Numbers, Standard Deviation, Regression Calculation, number systems in other bases and bitwise logical calculations are disabled.
   2. Press {  2  } for Complex Number Mode for working with imaginary and complex numbers. There are two different ways to display complex numbers which you can select here. This mode sets the "CMPLX"   state   indicator. The "R ⇔ I"   state   indicator in the upper right corner of a calculation result display indicates a complex result. Press the {  Re⇔Im  } key to toggle the display between the two parts of the result.
      Other keys that change in Complex Mode are: {  ∠  }, {  arg  }, {  Abs  }, {  Conjg  }, { » r∠θ  }, { » a+bi  }. The variables D, E, F, X, and Y are used by the calculator in this mode and are not available for you to use. You should only use the variables A, B, C, and M.
2.  MODE  key submenu: 1-SD   2-REG   3-BASE
   1. Press {  1  } to select  Standard Deviation Mode   and set the "SD"   state   indicator.
   2. Press {  2  } for  Regression Calculation Mode   and set the "REG"   state   indicator.
   3. Press {  3  } for  Base Mode  for Binary, Octal, Decimal, and Hexadecimal calculations and set the "d"   state   indicator.
3. MODE  key submenu: 1-EQN
   Press {  1  } to switch to the EQUATION MENU then use the {  →  } and the {  ←  } on the {  REPLAY  } Key to switch between two submenus. Note that the formats of the equations are different. Either selection will set the same "EQN"   state   indicator.
   • UNKNOWNS?   2 3
     Press {  2  } or {  3  } depending on how many unknowns you have in your system of  Linear Equations  
   • Degree?   2 3
     Press {  2  } or {  3  } to solve or factor second or third degree  polynomial equations  .
4.  MODE  key submenu: 1-Deg   2-Rad   3-Grad
   Press {  1  } to select Degrees,
   Press {  2  } for Radians,
   Press {  3  } for Grads as units for displaying angles.
   The three choices of units for displaying the measure of an angle are: Degrees (90 degrees = a right angle), Radians ( π/2 radians = right angle) or Grads (100 grads = right angle). This selects the Output or Display units and sets the DEG, RAD, or GRAD   state   indicator. The default input unit is the same as the output unit. You can specify a different input unit by using the {  DRG »  } key.
5.  MODE  key submenu: 1-Fix   2-Sci   3-Norm
   1. Press {  1  } to display a fixed number of places after the decimal point on the screen. Fix 0~9?
      Press { 0-9 } to select the number of digits to be displayed after the decimal point and set the "FIX"   state   indicator.
      Example: {  123.45678 = MODE MODE MODE MODE MODE FIX 3  }   [ 123.457 ]
      Note: Changing the number of digits that are displayed on the screen does not change the value inside the calculator. If you also want to change the value inside the calculator then you must use the {  Rnd  } key.
   2. Press {  2  } for scientific notation. Sci 0~9?
      Press ( 0-9 ) to select the number of digits to display (except that 0 displays 10 digits) and set the "SCI"   state   indicator.
      Example: {  123.45678 = MODE MODE MODE MODE MODE Sci 3  }   [ 1.23 × ₁₀⁰² ]
   3. Press {  3  } for normal format with a variable number of places after the decimal point. Norm 1~2?
      1. Press {  1  } to use scientific/exponential format for x ≥ 10¹⁰ or x < 0.01
      2. Press {  2  } to use scientific/exponential format for x ≥ 10¹⁰ or x < 0.000000001
6.  MODE  key submenu: 1-Disp
   Press {  1  } to switch to the DISPLAY MENU. Then you can use the {  →  } and the {  ←  } on the {  REPLAY  } Key to switch between sub-submenus:
   
   •  DISPLAY  sub-submenu: 1-EngON 2-EngOFF
     Press {  1  } to turn on Engineering display mode and set the "ENG"   state   indicator, or
     Press {  2  } to turn it off.
     Engineering display mode uses   engineering   units to display answers. You do not need to turn on the engineering display mode to enter Eng Units.

   •  DISPLAY  sub-submenu: 1-a+bi   2-r∠θ
     This submenu is only available in  Complex Number  Mode and it specifies the default format for displaying complex numbers. You can override the default by using either the { » a+bi  } or the {  » r∠θ  } key.
     Press {  1  } to select rectangular (also called Cartesian or Euclidean) coordinates in the form a+bi where a is the real part and b is the imaginary part of the Complex number.
     Press {  2  } for polar coordinates in the form r∠θ where r is the   absolute   value or distance from the origin and &theta is the argument or the   angle   that it makes. This key sets the "r∠θ"   state   indicator
     Note: This calculator does not handle complex numbers in exponential form like re^iθ.

   •  DISPLAY  sub-submenu: 1-ab/c   2-d/c
     Press {  1  } to select proper fraction display mode. A proper fraction is one in which the numerator is less than the denominator.
     Press {  2  } for improper fraction display mode.
     Warning: If you select this mode the calculator will give you a [ Math ERROR ] if you try to enter a fraction in the form (a b/c)
     Note: The {  SHIFT  }   {  d/c  } key will switch your answer between (a b/c) and (d/c) format.

   •  DISPLAY  sub-submenu: 1-Dot   2-Comma
     Press {  1  } to select US mode for displaying numbers [ 1,234,567.89 ]
     Press {  2  } for European mode [ 1 234 567,89 ]

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The {  SHIFT  }   {  CLR  } key

The CLR key gives you the following options: 1-Mcl   2-Mode   3-All
In SD MODE this changes to : 1-Scl   2-Mode   3-All

1. Press {  1  } to zero out all 9 variables
   • (A - F, M, X, Y)
   • ScL clears out the statistical accumulators
2. Press {  2  } to reset all Mode settings to their initial values:
   • Calculation mode:  COMP  
   • Angle units: Degrees
   • Exponential display format: Norm 1, Eng OFF
   • Complex Number Display Format: a + bi
   • Fraction Display Format: a^b/c
   • Decimal Point Character: Dot
3. Press {  3  } to clear both Memory and Mode settings.

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The {  ON  } key

This key turns the calculator on. The calculator has an Auto-Off function which turns the calculator off after six minutes of inactivity. If you want to turn the calculator off manually you can do this with the {  OFF  } key.

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The {  SHIFT  }   {  SOLVE  } key

To use this key you need to enter an equation using the {  =  } sign on the {  CALC  } key. After entering the equation press the {  SOLVE  } key and it will ask you for the values of each of the variables. Enter values for all but one of the variables using the other {  =  } key. Use the up/down scroll keys {  ↑  } and {  ↓  } to enter each value, then go back to the remaining variable and press the {  SOLVE  } key and WAIT. Note: It can take a very long time for the calculator to solve the equation.
For example, to solve the equation A = B² + C given A = 10 and C = 1 you would enter:
{  ALPHA  } {  A  } {  ALPHA  } {  =  } {  ALPHA  } {  B  } {  x²  } {  +  } {  ALPHA  } {  C  } {  SHIFT  } {  SOLVE  }
[A?] {  1  } {  0  } {  =  }
[B?] {  ↓  }
[C?] {  3  } {  =  }
{  ↑  } {  SHIFT  } {  SOLVE  }
WAIT a long time... the answer [ 3 ] will appear.

TIP: People who had trouble with this function were using the wrong key to enter the {  =  } sign. You MUST use the "solve / = / calc" key with {  ALPHA  } shift.

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The {  ALPHA  }   {  =  } key

Note: this key is totally different from the main {  =  } key.
Use this key when you want to enter an equation to be solved by the equation solver using the {   SOLVE  } key.

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The {  CALC  } key

The CALC key enables you to enter a formula or an expression and evaluate it by substituting values for the variables.
Example: {  B²-4AC  } {  CALC  }
B? {  3=  }
A? {  2=  }
C? {  1=  } [ 1 ]
If you press the {  =  } key again the calculator will go back into data entry mode and allow you to review or change the values of the variables.

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The {  SHIFT  }   {  d/dx  } key

uses the difference quotient ( ( f(x+h) - f(x) ) ÷  h ) to approximate the derivative. The function requires three inputs:

1. the function f(x)
2. the value of x
3. the value of h (optional, the calculator will pick one for you if it is not supplied.)

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The {  ALPHA  }   {  :  } key

This key allows you to enter a "multi-statement" which is the concatenation of more than one instruction in the same line. Another way to create a multi-statement is by using the Copy key. I believe it can probably be very useful. It seems that if you use the up arrow key after the execution of a multi-statement you get the individual statements that had been executed but if you use the left arrow key you get a chance to edit the multi-statement. There are some other idiosyncrasies but I haven't cared enough to figure them out.

Example: Here is a neat trick for generating pairs of data points automatically. Graph the function f(x)=x² - 3x + 2 in the interval from x = -1 to x = +3. Generate data points for values of x 0.5 units apart. We need to do two things at each step, calculate a y-value and get the next x-value. We will enter both of these statements into the calculator on one line and use a colon to separate them.
The finished program will look like this: {x²-3x+2:x=x+.5} where the {=} sign has to be entered with the {  ALPHA  }{  CALC  } key.
Here is the process:

1. Initialize x: {  -1  }{  SHIFT  }{  STO  }{  X  } [ -1 ]
2. Enter Program and get first y value: {  x²-3x+2:x=x+.5  }{  =  } [ 6 ]
   Note: The Disp indicator turns on during the execution of a multi line command. (Special thanks to Adam Sundor for telling me this.)
3. Calculate the next value of x by pressing the equal key: {  =  } [ -0.5 ]
4. Next value of y: {  =  } [ 3.75 ]
5. By continuing to press the {  =  } key we will alternate between values of x and y.

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The {  ∫ dx  } key

Use Simpson's rule to calculate an approximation to the integral. This key requires 4 input arguments:

1. the function being integrated,
2. the lower limit
3. the upper limit
4. a digit between 1 ... 9 specifying the accuracy. The higher the number the longer it will take to do the calculation.

 x=2
 ∫   ln(x)dx =  [ 0.386294361 ]
 x=1

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The {  SHIFT  }   {  x!  } key

calculates the factorial function. The factorial can only be calculated for integer values between 0 and 69. The factorial function is usually defined recursively as follows:
0! = 1
1! = 1
2! = 2 × 1!
n! = n × (n-1)!
Example:   {  5!=  }   [ 120 ]

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The {  logic  } key

This key is only available in  Base  MODE. Each time you press it, you will get a different menu:

1. 1-And   2-Or   3-Xnor
   Press {  1  } to select and enter the logical AND operator
   Press {  2  } for the OR operator
   Press {  3  } for the XNOR operator.
   XNOR is defined as "(A AND B) OR (NOT A AND NOT B)" which is the same as "NOT(A XOR B)" or "A EQUIV B"
2. 1-Xor   2-Not   3-Neg
   Press {  1  } to select and enter the logical Xor operator
   Press {  2  } for the Not unary operator
   Press {  3  } for the Neg unary operator.
3. 1-d   2-h   3-b   4-o These options allow you to override the default input number base
   Press {  1  } followed by a valid decimal value
   Press {  2  } followed by a valid hexadecimal value
   Press {  3  } followed by a valid decimal value
   Press {  4  } followed by a valid octal value

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The {  x^-1  } key

x^-1 calculates the reciprocal function which is the same as 1 ÷ x. Note that in this context the -1 is an actual exponent and not an inverse function. In other words this works like x² and gives the same result as pressing: {  ^  } {  (-)  } {  1  }
Example:   {  5^-1=  }   [ 0.2 ]

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The {  SHIFT  }   {  ³√  } key

calculates the cube root of the value.
Example:   {  ³√5=  }   [ 1.709975947 ]
Be sure to use parentheses if needed: {  ³√27+3=  } [ 6 ]     but   {  ³√(27+3)=  } [ 3.107232506 ]

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The {  x³  } key

calculates x × x × x
Can also be calculated with the exponent key by entering the key sequence: {  ^  } {  3  }
Example:   {  5³=  }   [ 125 ]

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The {  SHIFT  }   {  d/c  } key

After you have displayed an answer you can use this key to convert it to an improper fraction, or back to a proper fraction format.
Example 1:   [ 1 ¬ 2 ¬ 3 ] {  SHIFT  }   {  d/c  }   [ 5 ¬ 3 ]
Example 2:   [ 5 ¬ 3 ] {  SHIFT  }   {  d/c  }   [ 1 ¬ 2 ¬ 3 ]
Hint: You can use the {  a b/c  } key to convert fractions to decimal format.

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The {  a b/c  } key

This key can be used in two different contexts.

• When you are entering data it can be used to enter fractions.
  Example: {  1  } {  a b/c  } {  2  } {  =  } [ 1 ¬ 2 ] which is one half
• This key will also switch results between decimal format and proper fraction format.
  Example: [ 1 ¬ 2 ¬ 3 ] {  a b/c  }   [ 1.666666667 ]
  Hint: You can use the {  d/c  } key to convert it to an improper fraction format.

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The {  √  } key

Calculates the square root of a value. In  Computational  Mode you can not take the square root of a negative number. In  Complex Number  Mode you can get a complex result.
Can also be calculated with the exponent key by entering the key sequence: {  ^  } {  •  } {  5  }
Example:   {  ²√5=  }   [ 2.236067978 ]

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The {  DEC  } key

This key is only available in  Base  MODE. It converts the value shown in the display to Decimal (Base 10)and sets the "d"   state   indicator.

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The {  x²  } key

calculate the square or x × x.
Can also be calculated with the exponent key by entering the key sequence: {  ^  } {  2  }
Example:   {  5²=  }   [ 25 ]

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The {  SHIFT  }   {  ^x√  } key

calculate the x root. this is the inverse of the {  ^  } key.
Example:   {  ⁴√5=  }   [ 1.495348781 ]
In this course you need to know that rational exponents and that this is the same as the (x^-1) or the 1/x power.
So {  5  } {  ^  } {  (  } {  1  } {  ÷  } {  4  } {  )  } {  =  }   [ 1.495348781 ]

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The {  HEX  } key

This key is only available in  Base  MODE. It converts the value shown in the display to Hexadecimal (Base 16) and sets the "H"   state   indicator.

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The {  ^  } key

Raises a value to a specified power which can be an integer, a fraction or it can even be negative. The inverse of this function is the {  ^x√  } key
Example:   {  5^4=  }   [ 625 ]
Note: in  Complex Number  Mode this key is restricted. You can not use it raise a complex number to a power.
Example:   {  (2+i)  }{  x²  } and {  2 ^ 2  } are OK but {  (2+i) ^ 2  } is NOT.

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The {  SHIFT  }   {  10^x  } key

allows you to calculate any power of ten. This function is also known as the antilogarithm since its inverse is the function {  log  }
Example:  {  SHIFT  }   {  10^x  } {  1.5  }   {  =  } [ 31.6227766 ]

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The {  BIN  } key

This key is only available in  Base  MODE. It converts the value shown in the display to Binary (Base 2) and sets the "b"   state   indicator.

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The {  log  } key

Calculates the base 10 logarithm. The inverse of this function is the {  10^x  } key.
Example:   {  log(3)=  }   [ 0.477121254 ]

Note: To calculate a logarithm to some other base Use the formula:
^log_a^(b) = log(b) ÷ log(a)
^log₂⁽³⁾ is {  log(3)÷log(2)=  }   [ 1.584962501 ]
You can check this by entering {  2^1.584962501=  }   [ 3 ]

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The {  SHIFT  }   {  e^x  } key

calculates a power of  e  . This is the inverse of the natural logarithm function {  ln  } It is sometimes called the anti-logarithm.
Example: To calculate e^1.5 press:   {  SHIFT  }   {  e^x  } {  1.5  } {  =  }   [ 4.48168907 ]

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The {  OCT  } key

This key is only available in  Base  MODE. It converts the value shown in the display to Octal (Base 8) and sets the "o"   state   indicator.

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The {  ALPHA  }   {  e  } key

e is a constant like  π   which can not be represented with decimal digits. Its approximate value is 2.71828182845904523536028747135266249775724709369995957496696762772407663035354
For a more precise value you can click  here  

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The {  ln  } key

The ln key is the inverse of the {  e^x  } key and calculates the logarithm to the base  e  
Example:   {  ln(3)=  }   [ 1.098612289 ]

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The {  SHIFT  }   {  ∠  } key

This key is only available in  Complex Number  Mode and is used to enter a complex value in polar coordinates.
Example:   {  4  } {  SHIFT  } {  ∠  } {  9  } {  0  } {  =  }   [ 4i ]

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The {  ALPHA  }   {  A  } key

This key is used to refer to the variable A.
Example: To add the contents of variable A to 5 {  ALPHA  } {  A  } {  +  } {  5  } {  =  }
Note: In  Base 16 - HEX mode  use this key WITHOUT the {  ALPHA  } key to enter hexadecimal digits.

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The {  (-)  } key

This key is used for entering negative quantities.
Example 1: Add negative 3 to negative 4:
{  (-)  }{  3  } {  +  } {  (-)  }{  4  }{  =  } [ -7 ]
You can not use this key to subtract two numbers. For that you must use the {  -  } key.
Example 2: {  (-)  }{  3  }{  (-)  }{  4  }{  =  } gives: [ Syntax ERROR ]
The correct way to do this is {  (-)  }{  3  }{  -  }{  4  }{  =  }   [ -7 ]
Warning: Unlike Excel and some other calculators, this calculator assigns a lower precedence to the negative operator than other operations such as raising a value to a power. For example {  (-) 2 ^ 2 =  }   [ -4 ] THIS WILL GIVE YOU THE WRONG ANSWER ON A MATH TEST. If you haven't memorized all the differences between operator priorities in mathematics versus priorities on this calculator, your safest bet is to use parentheses whenever you have more than one operation in an expression. The previous example should be entered like this: {  ( (-) 2 ) ^ 2 =  }   [ 4 ]
Note: in  Base  16 (hexadecimal) Mode this key is used to enter the Hex digit A₁₆ (value 10)

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The {  SHIFT  }   {  ← ° ’ ”  } key

This key allows you to convert decimal values to sexagesimal values. Sexagesimal values can correspond to hours° minutes° seconds or degrees° minutes° seconds or any other base 60 numbering system.
Example: To convert 4.085° (degrees to degrees° minutes° seconds) {  4.085  } {  =  }   [ 4.085 ] {  SHIFT  }   {  ← ° ’ ”  }   [ 4° 5° 6 ]
Example 2: To convert three and a half hours (hours to hours° minutes° seconds) {  3.5  } {  =  }   [ 3.5 ] {  SHIFT  }   {  ← ° ’ ”  }   [ 3° 30° 0 ]
Note: The key is actually a toggle key - if you press it a second time it will convert the data back to decimal format. As far as I can see this is a totally useless key since you can use the {  ° ’ ”  } key without the shift to perform both of these functions.

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The {  ALPHA  }   {  B  } key

This key is used to refer to the variable B.
Example: To add the contents of variable B to 5 {  ALPHA  } {  B  } {  +  } {  5  } {  =  }
Note: In  Base 16 - HEX mode  use this key WITHOUT the {  ALPHA  } key to enter hexadecimal digits.

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The {  ° ’ ”  } key

This key can be used in two different contexts.

• It can be used to enter an angle in degrees° minutes° seconds format.
  Example: {  6  } {  3  } {  ° ’ ”  } {  5  } {  2  } {  ° ’ ”  } {  4  } {  1  } {  .  } {  8  } {  ° ’ ”  }   {  =  }   [ 63 ° 52 ° 41.8 ]
  Note 1: There is a discrepancy between how the data appears when you enter it and how it appears in the result screen. Every time you press the {  ° ’ ”  } key you will see a degree symbol on the formula entry line. In this example you must enter three ° symbols which will look like this on the formula line   [ 63° 52° 41.8° ] but when you press the {  =  } key you will only see two ° symbols on the result line:   [ 63°52°41.8 ]
  Note 2: Degrees° Minutes° seconds can also be read as Hours° Minutes° Seconds. This almost enables you to do time calculations except that instead of a 12 hour day or 24 hour day, there are no adjustments made for the end of the day. So 10:30 plus 4 hours is 14:30 and 21:30 plus 4 hours is 25:30.
  Example: If you add 3 hours and 45 minutes to 2:40 the answer is 6:25 {  3° 45° + 2° 40° =  }   [ 6° 25° 0 ]
• This key can also toggle the display between decimal format and degrees° minutes° seconds format.
  Example: [ 63°52°41.8 ] {  ° ’ ”  }   [ 63.87827778 ]
  Note: You can also use the {  SHIFT  }   {  ← ° ’ ”  } key to do the same thing.

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The {  ALPHA  }   {  C  } key

This key is used to refer to the variable C.
Example: To add the contents of variable C to 5 {  ALPHA  } {  C  } {  +  } {  5  } {  =  }
Note: In  Base 16 - HEX mode  use this key WITHOUT the {  ALPHA  } key to enter hexadecimal digits.

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The {  hyp  } key

This key is used to call the Hyperbolic and the Inverse Hyperbolic functions. When you press this key it turns on the hyperbolic   state   indicator.
To call inverse hyperbolic functions it doesn't matter in which order you press the {  hyp  } and {  SHIFT  } keys.
Example 1: sinh(3.6) = {  hyp  } {  sin  } {  3_•6  } {  =  } [ 18.28545536 ]
Example 2: sinh^-1(30) = {  hyp  } {  SHIFT  } {  sin^-1  } {  3_•6  } {  =  } [ 4.094622224 ]
or also {  SHIFT  } {  hyp  } {  sin^-1  } {  3_•6  } {  =  } [ 4.094622224 ]
These are the definitions of the hyperbolic functions:

                   ex - e-x
      sinh(x) = ------------
                      2

                   ex + e-x
      cosh(x) = ------------
                      2

                sinh(x)      ex - e-x
      tanh(x) = ------- =  ----------
                cosh(x)      ex + e-x

      coth(x) = 1/tanh(x)

      csch(x) = 1/sinh(x)

      sech(x) = 1/cosh(x) 

      sinh-1(x) = ln( x + √(x² + 1) )

      cosh-1(x) = ln( x + √(x² - 1) )

                   1      1 + x   
      tanh-1(x) = ---- ln -------
                   2      1 - x

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The {  SHIFT  }   {  sin^-1  } key

To change the default angle unit (degrees, radians, grads) see the {  MODE  } Key
To override the default angle unit see the {  DRG »  } key
Example:   {  sin^-1(.7)=  }   [ 44.427004 ]

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The {  ALPHA  }   {  D  } key

This key is used to refer to the variable D.
Example: To add the contents of variable D to 5 {  ALPHA  } {  D  } {  +  } {  5  } {  =  }
Note: In  Base 16 - HEX mode  use this key WITHOUT the {  ALPHA  } key to enter hexadecimal digits.

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The {  sin  } key

To change the default angle unit (degrees, radians, grads) see the {  MODE  } Key
To override the default angle unit see the {  DRG »  } key
Example (in degree mode): sin 63 ° 52 ’ 41 ”
{  sin  } {  6  } {  3  } {  ° ’ ”  } {  5  } {  2  } {  ° ’ ”  } {  4  } {  1  } {  ° ’ ”  } {  =  }   [ 0.897859012 ]
Note: in  Base  16 (hexadecimal) Mode this key is used to enter the Hex digit D₁₆ (value 13)

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The {  SHIFT  }   {  cos^-1  } key

To change the default angle unit (degrees, radians, grads) see the {  MODE  } Key
To override the default angle unit see the {  DRG »  } key
Example:   {  cos^-1(.7)=  }   [ 45.572996 ]

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The {  ALPHA  }   {  E  } key

This key is used to refer to the variable E.
Example: To add the contents of variable E to 5 {  ALPHA  } {  E  } {  +  } {  5  } {  =  }
Note: In  Base 16 - HEX mode  use this key WITHOUT the {  ALPHA  } key to enter hexadecimal digits.

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The {  cos  } key

To change the default angle unit (degrees, radians, grads) see the {  MODE  } Key
To override the default angle unit see the {  DRG »  } key
Example:   {  cos 5=  }   [ 0.996194698 ]
Note: in  Base  16 (hexadecimal) Mode this key is used to enter the Hex digit E₁₆ (value 14)

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The {  SHIFT  }   {  tan^-1  } key

To change the default angle unit (degrees, radians, grads) see the {  MODE  } Key
To override the default angle unit see the {  DRG »  } key
Example:   {  tan^-1(.7)=  }   [ 34.9920202 ]

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The {  ALPHA  }   {  F  } key

This key is used to refer to the variable F.
Example: To add the contents of variable F to 5 {  ALPHA  } {  F  } {  +  } {  5  } {  =  }
Note: In  Base 16 - HEX mode  use this key WITHOUT the {  ALPHA  } key to enter hexadecimal digits.

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The {  tan  } key

To change the default angle unit (degrees, radians, grads) see the {  MODE  } Key
To override the default angle unit see the {  DRG »  } key
Example:   {  tan 5=  }   [ 0.087488663 ]
Note: in  Base  16 (hexadecimal) Mode this key is used to enter the Hex digit F₁₆ (value 15)

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The {  SHIFT  }   {  STO  } key

This key allows you to store a value into one of the variables A, B, C, D, E, F, M, X, and Y. In {  Complex  } Mode you should only use the variables A, B, C, and M since the variables D, E, F, X, and Y are used by the calculator and are not available.
Note: when you press the {  STO  } key it turns on the "STO"   state   indicator and you do not have to press the {  ALPHA  } key. In addition it also performs the indicated calculation and stores the answer in Answer Memory   Ans   just like the {  =  } key.
Example: To store the value of 2 plus 3 into A Press: {  2 + 3  } {  SHIFT  } {  STO  } {  A  } [ 6 ]

Note 2: Special thanks to Paul Bonarrigo, P. E., for pointing out a strange side effect of this key. Most of the time if you unnecessarily press the {  =  } key in conjunction with {  SHIFT  } {  STO  } it is totally transparent and doesn't have any effect on your calculation. If you had pressed the {  =  } key in the last example like this: {  2 + 3 =  } and then pressed the {  SHIFT  } {  STO  } {  A  } you would still get the same answer of [ 6 ]. Paul showed me a situation where one actually gets an incorrect answer!

Let me paraphrase Paul's example:
Step one: Calculate 1+1 and leave the answer in Answer Memory: {  1 + 1 =  }   [ 2 ]
Step two: Multiply the answer by 3 and put the result into Variable Memory A: {  ×  } {  3  } {  STO  } {  A  }. The correct result will be stored in variable A as well as in the Answer Memory  [ 6 ]. The top line of the calculator will show: {  Ans × 3 → A  }
HOWEVER, if you get into the habit of (unnecessarily) pressing the {  =  } key you will end up storing an incorrect value into A.
Here's how it works. Let's say that in step two you use this sequence of keystrokes: {  × 3  } {  =  } {  STO  } {  A  } {  =  } then you will get the answer of 54. The reason for this is that you are actually recalculating the expression {  Ans × 3  } three separate times and each time you are updating the value of   Ans   Answer Memory.

• When you press the {  =  } key the first time you get the answer for {  Ans × 3  }, or 6, which is stored in the Answer Memory replacing the value of 2.
• When you press {  STO  } {  A  }, you are recalculating {  Ans × 3  } , which is now 6 × 3, and the value 18 is stored in variable A and Answer Memory.
• Pressing the {  =  } key at the end causes the calculator to re-execute the entire instruction {  Ans × 3 → A  } with the latest value for   Ans   which is now 18 and storing the result of 54 into variable A and the Answer Memory.

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The {  RCL  } key

Pressing this key sets the "RCL"   state   indicator and lets you display the value of a variable without having to press the {  ALPHA  } key.
Example:   {  RCL  }{  A  } displays the value of the variable  A  

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The {  SHIFT  }   {  ←ENG  } key

This key takes a result and displays it as a value in the range (.010-9.99) multiplied by a power of ten that is divisible by three. Look at the {  ENG  } key which shifts the value into a different range.
Example: [ 1234567890 ] {  SHIFT  }   {  ← ENG  }   [ 1.23456789 ×₁₀⁰⁹ ]
Pressing the {  ←ENG  } key additional times divides the scale by 1000 each time until the result would be zero.

Actually the whole thing makes a lot more sense if you turn engineering units   display   on.

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The {  i  } key

This key is only available in  Complex Number  Mode and is used for entering the imaginary number i.
Note: This key looks like it would use the {  ALPHA  } key. It doesn't. However you can use it either with or without the {  SHIFT  } key.

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The {  ENG  } key

This key takes a result and displays it as a value in the range (1-999) multiplied by a power of ten that is divisible by 3. Look at the {  SHIFT  }   {  ←ENG  } key which shifts the answer into a different range.
Example: [ 1234567890 ] {  ENG  }   [ 1.23456789 ×₁₀⁰⁹ ]

Each additional press of the key multiplies the range by 1000 until the result would exceed ten digits.

Actually the whole thing makes a lot more sense if you turn engineering units   display   on.

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The {  (  } and {  )  } keys

Parentheses serve to group a portion of an expression into a separate basket which is evaluated before things that are outside the basket. In this way they serve to change the natural order of operations.
Example 1: {  2×3+4=  }   [ 10 ]
Example 2: {  (2×3)+4=  }   [ 10 ]
Example 3: {  2×(3+4)=  }   [ 14 ]

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The {  SHIFT  }   {  arg  } key

This key is only available in  Complex Number  Mode. It calculates the argument of the complex number - that is it calculates the principle angle θ in the polar coordinates representation of a complex number.
Example: {  arg(3+4i)=  }   [ 53.13010235 ] since 3+4i is equal to 5∠53.13010235 in r∠θ form. See {  Abs  } for the value of r or {  » r∠θ  } to get both values.

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The {  ALPHA  }   {  X  } key

This key is used to refer to the variable X.

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The {  SHIFT  }   {  Abs  } key

This key is only available in  Complex Number  Mode and calculates the polar r coordinate for a complex number. The coordinate r is the absolute value of a + bi which is given by r = √(a² + b²)
Example: {  abs(3+4i)=  }   [ 5 ] since 3+4i is equal to 5∠53.13010235. in r∠θ form. See {  arg  } for the value of θ or {  » r∠θ  } to get both values.

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The {  SHIFT  }   {  ;  } key

This key allows you to enter multiple occurrences of the same data point in  Standard Deviation  and  Regression  calculations.

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The {  ALPHA  }   {  Y  } key

This key is used to refer to the variable Y

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The {  ,  } key

This key separates the parameters in a multi parameter function.

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The {  SHIFT  }   {  Conjg  } key

This key is only available in  Complex Number  Mode. It calculates the complex conjugate of a value.
Example: {  Conjg(1+2i)=  }   [ 1 ]
{  SHIFT  }   {  Re⇔Im  }   [ -2_i ]

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The {  SHIFT  }   {  M-  } key

This Key allows you to subtract from memory M.
To see how this key might be used, see the Example that follows the {  M+  } key.

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The {  ALPHA  }   {  M  } key

This key is used to refer to the variable M.
Memory M is a special location. To see how it is used, see the Example that follows the {  M+  } key. Whenever the contents of this location are non zero the "M"   state   indicator is turned on.

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