If \( \alpha \) is the \( n^{\text {th }} \) root of unity, then \( 1+2 \alpha+3 \alpha^{2}+\ldo...

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If 1,α,α^2,α^3⋯⋯α^n 1 be the nth root of unity, then 1^P+α^P+(α^2 )^P+(α^3 )^p+⋯⋅(α^(n-1) )^P= If 1,α,α^2,α^3⋯⋯α^n 1 be the nth root of unity, then 1^P+α^P+(α^2 )^P+(α^3 )^p+⋯⋅(α^(n-1) )^P=
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