# Proving an identity in mathematics

Show that if z0 is an nth root of unity(z0 is not equal to 1) then

1+z0+z0^2+...+z0^(n-1)=0.

Hence show that

cos(2Pi/1998)+cos(4Pi/1998)+...+cos(2Pi*1997/1998)=-1

https://brainmass.com/math/complex-analysis/proving-identity-mathematics-5005

#### Solution Preview

Proof: Since z0 is an nth root of unity, z0^n=1.

So

(z0-1)(z0^(n-1)+z0^(n-2)+...+1)=0.

Since z0 ...

#### Solution Summary

The solution contains a detailed proof of an equality involving the n-th root of unity.

$2.49