Question

How can you use trigonometric functions to simplify `23 e^( ( 2 pi)/3 i )` into a non-exponential complex number?

Answer 1

-11.5 + i 11.5`sqrt`3)

Explanation:

The polar form of a complex number (x, y) = x + i y is r `e ^(i theta)` = r (cos(`theta`) + i sin (`theta`)). Here, r = 23 `and theta` = 2`pi`/3. cos (`2pi`/3) = cos (`pi - pi/3`) = - cos (`pi/3`) and sin (`2pi`/3) = sins (`pi - pi/3`) = sin (`pi/3`).