If `alpha, beta` are the complex cube roots of unity then `alpha^100 + beta^100 + 1 / (alpha^100 xx beta^100)=`

If alpha and beta are the complex cube roots of unity, then show that alpha^4 + beta^4 + alpha^-1beta^-1 = 0

If alpha and beta are the complex cube roots of unity, show that alpha^4+beta^4 + alpha^-1 beta^-1 = 0.

If alpha and beta are the complex cube roots of unity, then show that alpha^2 + beta^2 + alphabeta = 0

If alpha and beta are complex cube roots of unity, show that alpha^2 + beta^2 + alpha beta =0

If alpha , beta are the imaginary cube roots of unity then alpha^(4) + beta^(4) - (alpha + beta)^(4) =

If alpha and beta are the complex cube root of unity, show that alpha ^(4) + beta ^(4) + alpha ^( -1) beta ^(-1) = 0

If alpha and beta are complex cube roots of unity, show that alpha^4 + beta^4 + alpha^(-1) beta^(-1) =0

If alpha and beta are complex cube roots of unity, then (1-alpha)(1-beta)(1-(alpha)^2)(1-(beta)^2) =

If alpha and beta are the complex cube roots of unity, then prove that (1 - alpha) (1 - beta) (1 - alpha^2) (1 - beta^2) = 9 .