Prove Nth Roots of Unity: \omega, \overline{\omega}, \omega^{r}

[gotmilk04]

Homework Statement

Show that, if \omega is an nth root of unity, then so are \overline{\omega} and \omega^{r} for every integer r.

Homework Equations

\omega=r^{1/n}e^{i((\theta+2\pi)/n)}

The Attempt at a Solution

I got the first part and for \omega^{r} I have it equals
e^{i(r2\pi/n)}
but what more do I need to do/show to prove it's an nth root of unity?

 

[Dick]

There's no need to use an explicit form for w. An nth root of unity satisfies w^n=1. Just use that. Take the conjugate and then raise both sides to the power r.