Question

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

Answer 1

Answer:

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