> 
> Let $z$ be a complex number such that
> $$
> z + \frac{1}{z} = \cos x
> $$
> Then what is the value of the expression
> $$
> z^n + \frac{1}{z^n}
> $$
> where $n$ is an integer?
> 
> 
> 

Please help me. I have tried somehow using the trigonometric way of defining complex numbers but still didn't manage to get anywhere.