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:

![https://www.google.com/search?q=demorvies+theorem&client=safari&hl=en-us&prmd=ivn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiYmuTisNLbAhWJwI8KHXycAGsQ_AUIESgB&biw=768&bih=922#imgrc=XMEZvta0Lgq8wM:]()

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`