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]

 Mar 18, 2023
edited by Melody  Mar 19, 2023
edited by Melody  Mar 19, 2023

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