Question

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

Answer 1

By using the Moivre formula.

Explanation:

The Moivre formula tells us that `e^(itheta) = cos(theta) + isin(theta)`. You apply it here !

`3e^(i(2pi)/3) = 3(cos((2pi)/3) + isin((2pi)/3)) = 3(-1/2 + sqrt(3)/2) = -3/2 +(3sqrt(3))/2`