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 + w ^(2)) ^( 5) + (1 + w - w ^(2)) ^( 5) = 32

If w is a complex cube root of unity, prove that (1 - w + w ^(2)) ^(6)+(1 + w - w ^(2)) ^(6) = 128

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 prove that (1 + w ^(2)) ^(3) =- 1

If w is a complex cube root of unity, then prove that (1- w + w ^(2)) ^(3) =-8

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