# Nth roots of unity

1. Sep 13, 2009

### gotmilk04

1. The problem statement, all variables and given/known data
Show that, if $$\omega$$ is an nth root of unity, then so are $$\overline{\omega}$$ and $$\omega^{r}$$ for every integer r.

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

3. 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?

2. Sep 13, 2009

### 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.