Texas Instruments TI-83 $$

2-16 Math, Angle, and Test Operations

8302MATH.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:12 PM Printed: 02/19/01 2:27

PM Page 16 of 26

The TI-83 displays complex numbers in rectangular form

and polar form. To select a complex-number mode, press

z, and then select either of the two modes.

• a+bi (rectangular-complex mode)

• re^qi (polar-complex mode)

On the TI-83, complex numbers can be stored to variables.

Also, complex numbers are valid list elements.

In Real mode, complex-number results return an error,

unless you entered a complex number as input. For

example, in Real mode ln(L1) returns an error; in a+bi mode

ln(L1) returns an answer.

Real mode a+bi mode

Complex numbers are stored in rectangular form, but you

can enter a complex number in rectangular form or polar

form, regardless of the mode setting. The components of

complex numbers can be real numbers or expressions that

evaluate to real numbers; expressions are evaluated when

the command is executed.

Radian mode is recommended for complex number

calculations. Internally, the TI-83 converts all entered trig

values to radians, but it does not convert values for

exponential, logarithmic, or hyperbolic functions.

In degree mode, complex identities such as

e^(iq) = cos(q) + i sin(q) are not generally true because

the values for cos and sin are converted to radians, while

those for e^() are not. For example,

e^(i45) = cos(45) + i sin(45) is treated internally as

e^(i45) = cos(p/4) + i sin(p/4). Complex identities are

always true in radian mode.

Complex-Number

Modes

Entering

Complex

Numbers

Note about

Radian versus

Degree Mode