1. ## Complex Numbers Problem

I'm not sure what section to place this in.. but here it goes!

How would I go about showing the following?:

Show that if z is any nth root of unity other than unity itself, then
$1 + z + z^{2} + z^{3} + ... + z^{n - 1} = 0$

Thanks,

James Elmore

2. Originally Posted by jameselmore91
I'm not sure what section to place this in.. but here it goes!

How would I go about showing the following?:

Show that if z is any nth root of unity other than unity itself, then
$1 + z + z^{2} + z^{3} + ... + z^{n - 1} = 0$

Thanks,

James Elmore
Consider the solution to $z^n - 1 = 0$ by first factorising $z^n - 1$.