Sum of n-th roots of a complex number equals zero

[JasonPhysicist]

Homework Statement

I'd like some help with 2 problems:

Show by using Demoivre's theorem and the geometric series formula that the sum of all n values of z^(1/n) is zero when n >=2.
Z is a complex number.

Use the geometric series formula and Demoivre's theorem to show that:

Homework Equations

the geometric series formula:

Demoivre's theorem

The Attempt at a Solution

For the first part,I've tried to make z^(1/n) = p so that p^n = z ,but I had no success showing that the sum equals zero...
For the second part I've made z= cos(theta) + i sin(theta) and I've obtained the left part of the formula,but I can't get the right part...

I'd appreciate any help,because I don't seem to be going anywhere.
Thank you in advance!

 

[Mark44]

If $z = cos(\theta)$, what is z², z³, and so on?

 

[andylu224]

For the second question, a big hint is to equate equivalent terms.

a + bi = c + di --> a = c, b = d

Don't move things across the equals sign, but work on each side separately