Question

z^5 = -1

Answer 1

Complex roots... I haven't done these in a while :D

Answer 2

So you're basically looking for all fifth roots of -1, am I right? :D

Answer 3

First, you need to express -1 in polar form.

Answer 4

z is the 5th root of -1.
odd root of -1 is -1
even root of -1 is a complex number
since 5 is odd z=-1

Answer 5

Well, certainly, -1 is a fifth root of -1, but there are others...
For instance,
\[\Large \cos(36^o) + \color{blue}i\sin(36^o)\]