Find all complex numbers satisfying z^6=1
"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?