Find all complex numbers satisfying z^6=1

Hi guys.

"Find all complex numbers satisfying "

The hint is to factorise as a difference of squares.

This seems incorrect.

The bracketed terms are not quadratics of standard form and two z terms are identical, leading only to five solutions, from what I can see.

I've seen a solution involving De Moivre's theorem, in which a full rotation is split into six pieces, taking the where .

I'm very interested in understanding the solution with De Moivre's theorem. It was explained in a course I took last semester but I simply cannot remember a thing about it.

I've asked several people about this problem, but they can't seem to distinguish copying from understanding.

I would love to really understand the solution to this problem.

Can you help?