# How can you use trigonometric functions to simplify # 22 e^( ( 3 pi)/4 i ) # into a non-exponential complex number?

##### 1 Answer

See details below.

#### Explanation:

Following expressions have the same value

where

(The angle of the point on the complex plane obtained by taking inverse tangent of the complex portion over the real portion)

The question asks us to change from exponential form using trigonometric functions. Therefore, let's chose to change from exponential form to polar form.

Polar* form becomes

Inserting the value of cosine and sine of the angle

Expressing in rectangular* form

*Both Polar Form and Rectangular Form the are required non-exponential complex numbers