Solving a complex equation with roots of unity

Clouded

1. The problem statement, all variables and given/known data

z is a complex number.

Find all the solutions of

(z+1)^5 = z^5

3. The attempt at a solution

Of course one could expand (z+1)^5, but I remeber our professor solving this with roots of unity. Can anyone help?

Clouded

Ah, embarissing.

1=(z+1)^5/z^5
=((z+1)/z)^5

and then just using the roots of unity to find z= 1/(1-w) , w=exp(i*2k*pi/5), k=1,2,3,4.