Working with Complex Numbers on the TI-83
Prepared by Mike Shannon edited by T. G. Cleaver 4/12/2004

1.  Rectangular to Polar Conversion
Set Mode to Degrees and Normal.
Type in the rectangular form as (a + bi), where a is the real part and b is the imaginary part.
Press math button.
Select CPX.
Scroll down to 7.
Activate function.
Answer is in exponential form (Meθi) where M is the magnitude and θ is the angle (in degrees).
You can then write the answer in polar form M.
Note that the TI-83 cannot display polar form.

2.  Polar to Rectangular Conversion
Set Mode to Degrees or radians (doesn't matter) and Normal.
Type in the exponential form as (Meθi), where M is the magnitude and θ is the angle in radians (Note that the TI-83 requires the angle in radians even when set in degrees mode).
Note that the TI-83 cannot display polar form.

Press math button.
Select CPX.
Scroll down to 6.
Activate function.
Answer is in rectangular form as (a + bi), where a is the real part and b is the imaginary part.

3.  Complex Number Arithmetic
Set Mode to Radians and Normal.
Note that the TI-83 requires angles in radians for complex math.
Type in the mathematical expression.  The terms can be in rectangular form (a + bi), where a is the real part and b is the imaginary part, and exponential form as (Meθi), where M is the magnitude and θ is the angle (in radians).
Example:

(6/19°)(40 + 51i)/[(2 - 7i)(5/-147°)] should be entered as:
(6e^(19pi/180i))(40 + 51i)/((2 - 7i)(5e^(-147pi/180i)))
The answer should be 3.99 - 9.9i