If alpha and beta are complex cube root of unity prove that (1+α)×(1+beta)×(1+alpha)2(1+beta)2=1

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If alpha and beta are complex cube root of unity prove that (1+α)×(1+beta)×(1+alpha)2(1+beta)2=1

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Charlie 1 month 2021-09-15T01:14:26+00:00 1 Answer 0 views 0

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    2021-09-15T01:16:23+00:00

    Answer:

    we \: know \: that \: 1 +  \alpha  +  \beta  = 0 \: and \:  \alpha  \beta  = 1 \: now \: 1 +  \alpha  =  -  \beta  \: and \: 1 +  \beta  =  -  \alpha  \: so \: lhs. \: ( -  \beta )( -  \alpha )( -  \beta ) {}^{2} ( -  \alpha ) {}^{2}  = ( \alpha  \beta ) {}^{3}  = 1 \: rhs \:. \: proved.

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