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 (Me^{θi})
where M is the magnitude and θ is the angle (in degrees).

You can then write the answer in polar form M__/θ__.

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 (Me^{θi}),
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 (Me^{θi}),
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