" 21.If "w" is a complex cube root of unity,show that "

If w is a complex cube-root of unity then,

If w is a complex cube root of unity, show that (1 + w - w ^(2))^(6) = 64

If w is a complex cube root of unity, then show that (1-w) (1- w ^(2)) (1 - w ^(4)) ( 1 - w ^(5)) = 9

If w is a complex cube root of unity, then show that (1 - w + w ^(2)) ^( 5) + (1 + w - w ^(2)) ^( 5) = 32

If w is a complex cube root of unity, show that ([[1,w,w^2],[w,w^2,1],[w^2,1,w]]+[[w,w^2,1],[w^2,1,w],[w,w^2,1]])*[[1],[w],[w^2]]=[[0],[0],[0]]

If omega is a complex cube root of unity, show that (a+b) + (a omega +b omega^2 )+(a omega^2 +b omega ) =0