What Are the Roots of z^n = -1 in Complex Numbers?

[sara_87]

Homework Statement

What are the roots of

z^n = -1

Homework Equations

The Attempt at a Solution

are they

$$e^{\frac{2\pi k i}{n}-\frac{i \pi}{n}}$$

?

 

[lanedance]

sounds reasonable

 

[jeppetrost]

if by k you mean "all integer values k in [0,n[" then yes, that is correct, which in turn implies n nth roots.