Question

How do you use DeMoivre's theorem to simplify `(2e^(30i))^3`?

Answer 1

`8[cos (90 - 28 pi) + i sin (90 - 28 pi)]`

Explanation:

`e^(it) = cos t + i sin t`

`X = 2^3(cos 30 + i sin 30)^3`

`= 8(cos 90 + i sin 90)`

`14 * 2pi = 87,9645943...`