Question

How can you use trigonometric functions to simplify `27 e^( ( 5 pi)/3 i )` into a non-exponential complex number?

Answer 1

You use Euler's Formula

Explanation:

Euler's Formula states that `e^(itheta)=cos(theta)+isin(theta)` Using trigonometry, you can readily see that `x=cos(theta) and y=sin(theta)`. Hence, for your question, `27e^((5pi)/3i)=27(1/2-sqrt(3)/2i)` .

Edit: Plugged in the wrong values originally. Now fixed.