If `alpha` and `beta` are complex cube roots of unity, show that `alpha^2`+`beta^2`+`alpha``beta` =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^4 + beta^4 + alpha^(-1) beta^(-1) =0

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 root of unity, show that alpha ^(4) + beta ^(4) + alpha ^( -1) beta ^(-1) = 0

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

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 complex cube roots of unity. Prove that (1- alpha) ( 1- beta) (1- alpha ^(2)) (1 - beta ^(2)) = 9

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 .

If x=a+b, y=a alpha + beta b and z=a beta +b alpha where alpha and beta are complex cube roots of unity then show that xyz = a^3 + b^3 .