How to Prove z^n + 1/z^n = 2cos(nθ) Using Induction?

[mikee]

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 I am 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

 

[olgranpappy]

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 I am 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]

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