Question

How do you use DeMoivre's Theorem to simplify `(cos0+isin0)^20`?

Answer 1

`color(indigo)(cos 0 + i sin 0)^(20) = cos (20*0) + i sin (20*0) = 1`

Explanation:


By De Moivre’s theorem,

`z = [r(cos theta + i sin theta)]^n = r^n (cos ntheta + i sin btheta)`

`(cos 0 + i sin 0)^(20) = cos (20*0) + i sin (20*0) = 1` as

`cos 0 = 1, sin 0 = 0 & r = 1`