Roots of Unity

So I have a problem regarding roots of unity.

I have that |z|^n=1 and |z+1|^n=1.

I'm supposed to find the exponential form for the possible values of z.

For the first one, I got   $e^{(2\pi ki)/n}$    with both k and n being positive integer values.

I have no idea how to write the exponential form for (z+1)^n.

Could I say like     $z = e^{(2\pi)} - 1$?

But like, wouldn't -1 need to be simplified? How do I do that?

As a follow up question, how can I prove n must be divisible by 6? 

Thank you in advanced!

[Question cleaned up by Melody]