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If 1,alpha,alpha^2,…,alpha^(n-1) are the...

If `1,alpha,alpha^2,…,alpha^(n-1)` are the `n^(th)` roots of unity show that `sum_(r=1)^(n-1)r(alpha_r+alpha_(n-r))=-n`.

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The correct Answer is:
`=n{alpha_1+alpha_2+alpha_3+…....+alpha_(n-1)=n{-1}=-n`
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