How can you use trigonometric functions to simplify # 22 e^( ( 3 pi)/4 i ) # into a non-exponential complex number?
See details below.
Following expressions have the same value
(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