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Let alpha=cos(2pi)/n+isin(2pi)/n , n in ...

Let `alpha=cos(2pi)/n+isin(2pi)/n , n in N` and let `A_k=x+y alpha^k+z alpha^(2k)+...+walpha^((n-1)k)` where `(k=0,1,2,...n-1)` where `x,y,z,...,u,w` are n arbitrary complex numbers. Prove that `sum_(k=0)^(n-1) |A_k|^2=n{|x|^2+|y|^2+|z|^2+...+|w|^2}`

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