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.