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, show that (1 + w - w ^(2))^(6) = 64

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

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

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