# Homework Help: Complex numbers and induction

1. Sep 20, 2008

### mikee

1. The problem statement, all variables and given/known dataIf z is a non-real complex number such that z+1/z=2costheta, prove that z^n+1/z^n=2cosntheta for any posistive integer n

2. Relevant equations
I think the process of induction would work, but im not quite sure how to do that with all of the unknowns, would i just treat costheta as a constant number

3. The attempt at a solution

2. Sep 20, 2008

### olgranpappy

Apparently
$$z=e^{i\theta}$$
...does that help?

3. Sep 20, 2008

### rock.freak667

If z=cosx+isinx, what is z^n?