Question

How can you use trigonometric functions to simplify `17 e^( ( 4 pi)/3 i )` into a non-exponential complex number?

Answer 1

`-`17/2 ( 1 + `sqrt`3 i)

Explanation:

r = 17, `theta` = `4pi/3`
In non-exponential form x + i y,
x = r cos `theta` and y = r sin `theta`.
Also, cos ( `pi` + `theta`) = `- cos theta` and sin ( `pi` + `theta`) = `- sin theta`.