not sure if this is the right forum so sorry if i got it wrong. i'm having alot of trouble with this question. the numbers in brackets in front of the w's are meant to be subscripts

if $\displaystyle w_n = \exp\left(2\pi i/n\right)$ show $\displaystyle w_n^n = 1$ and that

$\displaystyle 1 + w_n +w_n^2 + w_n^3 + \dots + w_n^{n-1} = 0$

and show

$\displaystyle \left(x + y\cdot w_3 + z\cdot w_3^2\right)\left(x + y\cdot w_3^2 + z\cdot w_3\right) = x^2 + y^2 +z^2 - xy -yz -zx$

sorry for the lack of tex in it. thanks so much for any help given!!

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Edit by Chris L T521:Reformatted question with $\displaystyle \text{\LaTeX}$. Please inform me if I have misinterpreted anything.