# Math Help - Roots of unit complex numbers

1. ## Roots of unit complex numbers

Show that if $\omega$ is an $n$th root of unity ( $\omega \neq 1$ and $n>1$) then:

$\omega+\omega^2+...+\omega^n=0$

Would you do this (sum of G.P.)

$\omega\left(\dfrac{\omega^n -1}{\omega -1}\right)$

Since $\omega^n=1 \Rightarrow \omega^n-1=0$

$\Rightarrow \omega\left(\dfrac{\omega^n -1}{\omega -1}\right)=0$

2. Looks good to me.