# Calculator Tips

This page contains information about how to use various calculators for different classes.

# Complex Numbers

TI 83 plus, 84 plus, and 89 are all capable of dealing with complex numbers, but in different ways. Below, "83" means 83 plus and "84" means 84 plus.

## Entering Values

### Cartesian

- The 83, 84, and 89 all have the . For 83/84 it is "<2ND> ." and for the 89 it is "<2ND> <CATALOG>"; entering a complex number in Cartesian form is thus as simple as multiplying the imaginary part by .

### Euler

- The 83, 84, and 89 all allow for complex exponentials. Note, however, that the exponent
**must**be in radians, regardless of the mode of the calculator! The Euler form of would thus be .- For the 83, if you are in degree mode, the
*results*will be in degree mode but the inputs must always be in radians. For instance,

- For the 83, if you are in degree mode, the

e^(i*90)

returns

1e^(116.62i)

if the calculator is in degree mode since 90 radians simplifies to 116.62 degrees. It returns

1e^(2.035i)

if the calculator is in radian mode since 90 radians is the same as 90-28 is 2.035 radians.

- For the 84, the results are the same as for the 83
**however**you must be**very careful**if you try to use the result from a complex calculation that is reported in degree mode. On an 84, if you enter

- For the 84, the results are the same as for the 83

e^(i*90)

the result, in degree mode, is

1e^(116.62i)

If you try to up-arrow to that result and hit <ENTER> to copy it, then use it, the 84 will think of the 116.62 as a value in **radians** - which is to say, not at all what you meant! If you are in degree mode, you need to refrain from using the Euler representation on an 84 or at least understand that intermediate results in Euler mode and degree mode together cannot be used later.

- For the 89, the calculator will not let you use Euler representation if you are in degree mode - you will get a domain error. To use Euler representations on an 89, you will have to be in radian mode.

### Polar

- Neither the 83 nor the 84 use polar representation. You have to use Euler if you have a magnitude and an angle, and the angle must be entered in radians.
- The 89 has an angle button; to enter a complex number in polar notation, surround it with parentheses and separate the magnitude from the angle with the angle button, obtained with <2ND> <EE>. Note that the number you put in for an angle is based on the mode the calculator is in, so if you are in degree mode,

(1<60)

will be the same as

0.5+0.8660i

## Storing Values

If you are asked to perform complex calculations, you may want to store element values so that you can simply type a letter versus entering a number every time you use those values. For example, if a problem asks you to calculate the value of:

for a few different values of (say, 10 rad/s and 100 rad/s), you could do the following on your calculator:

```
1e-3 <STO>> <ALPHA> l
5e3 <STO>> <ALPHA> r
```

To store the frequency component, on TI 83/84 plus, you will need to use ALPHA z, while on the TI 89 you can just use the z button:

```
10 * 2ND i STO> (ALPHA) z
```

to store the values. Then, to calculate the first value,

```
( <ALPHA> z * <ALPHA> l ) / ( <ALPHA> z * <ALPHA> l + <ALPHA> r )
```

Once you get the result, if you want to calculate the value for a different frequency, simply type

```
100 * <2ND> i <STO>> <ALPHA> z
```

then use the arrow buttons to go back up to where you performed the previous symbolic calculation, ENTER it to duplicate it, then ENTER it again to calculate.

## Constant of Angle Conversion

If you are doing several complex calculations on an 83/84 and the angles you are given are in degrees, you may want to store a constant for the conversion to radians so you do not have to type in "* pi / 180" every time. You could just put in

pi / 180 <STO>> X

and then when you need to write a complex number in Euler form, you could multiply the angle in degrees by X; for instance, to get 6<30 degrees, you could write

6*e^(i*30*X)

You can choose any letter, obviously, but X is easy to get from the button on the 83/84.

# Statics Functions

## TI-83/84

Not as many built-in functions for vectors / matrices. See http://www.tc3.edu/instruct/sbrown/ti83/vecprod.htm for a program that will help with cross products.

## TI-89

### Vectors in General

Vectors may be entered surrounded by [ ]. That is, for some vector :

say,

the TI version of the vector would be:

[3, -2, 6]

Note that the result will actually be surrounded by two sets of square brackets, representing a matrix. Be sure to use the unary negative operator (-) versus the binary subtraction operator - at the start of negative entries.

### Dot and Cross Products

- Vector operations on TI Calculators: www.phys.lsu.edu/classes/spring2010/phys1100/TI_calc_vec.pdf

### Unit Directions

- To find the unit direction for a vector, use
- <2nd>--<5>MATH--<4>Matrix--L:Vector ops--<1>unitV()

### Coordinate Angles

- To find the coordinate angles of a vector, you should first get the unit direction vector. Then, you must turn the unit direction vector into a list before taking the arccos of the list. Lists are surrounded by {} instead of []. To convert a vector to a list, use
- <2nd>--<5>MATH--<3>List--F:mat->list()

and put the desired matrix in as the argument; the result will be surrounded by {}. You can then apply the arccos to the list and get all three coordinate direction angles at once!

- <2nd>--<5>MATH--<3>List--F:mat->list()

# Questions

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# External Links

- Complex Numbers on TI-83/84 by Stan Brown