# Complex numbers and induction

## Homework Statement

If 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

## Homework 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

## The Attempt at a Solution

Related Calculus and Beyond Homework Help News on Phys.org
olgranpappy
Homework Helper

## Homework Statement

If 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

## Homework 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

## The Attempt at a Solution

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

rock.freak667
Homework Helper
If z=cosx+isinx, what is z^n?