Algebraic Application invovling de Moivre's Therom

I don't really understand some examples I have been working through in finding the roots of complex numbers. One of the examples I am encountering problems with is:

z^6= -1

I am aware that I have to use the formula:

w = (mod z)^1/n cis ((theta + 2kpi)/n).

If I could get a quick worked example it would be much appreciated.

Edit: I think the main problem i am having finding the values for mod z and theta and not actually applying the formula.

It might help to write -1 as -1+0i. Then just use:




You will need to ensure that the angle is in the correct quadrant.