If 1, `omega omega^(2)` are the cube roots of unity show that `(1 + omega^(2))^(3) - (1 + omega)^(3) = 0`

If 1, omega, omega^(2) are the cube roots of unity, prove that (1 + omega)^(3)-(1 + omega^(2))^(3)=0

If 1, omega, omega ^(2) are the cube roots of unity , then w^2=

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8

Given that 1, omega, omega^(2) are cube roots of unity. Show that (1- omega + omega^(2))^(5) + (1 + omega - omega^(2))^(5)= 32

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If 1, omega, omega^(2) are three cube roots of unity, prove that omega^(28) + omega^(29) + 1= 0

If omega is a complex cube root of unity, then show that: (1 + omega)^3 - (1 + omega^2)^3 = 0

If 1, omega , omega^2 are cube roots of unity prove that (1 / (1 + 2omega)) - (1 / (1 + omega)) + (1 / (2 + omega)) = 0