Question

How do I use DeMoivre's theorem to find `(1-i)^10`?

Answer 1

`-32i`

Explanation:

First write this complex number in polar form and then apply De Moivre :

`(1-i)^10=(sqrt2/_-pi/4)^10=[sqrt2(cos(-pi/4)+isin(-pi/4))]^10`

`=(sqrt2)^10[cos(-10pi/4)+isin(-10pi/4)]`

`=-32i`