If `omega` is a complex cube root of unity, then show that: `(3 + 3omega + 5omega^2)^6 - (2 + 6omega + 2omega^2)^3 = 0`

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

If omega is a complex cube root of unity, then show that: (2 - omega) (2 - omega^2) = 7

If omega is a complex cube root of unity, then show that: (2 + omega + omega^2)^3 - (1 - 3omega + omega^2)^3 = 65

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

If omega is a complex cube root of unity, then show that: (a + bomega + comega^2) / (c + aomega + bomega^2) = omega^2

If omega is a complex cube roots of unity then show that following. (1 + omega - omega^2) ( 1 - omega + omega^2) = 4

If omega is a complex cube root of unity, show that (3+3 omega+5 omega^2)^6 - (2+6omega+2 omega^2)^3 =0

If omega is a complex cube roots of unity then show that following. (3 + 5omega + 3omega^2)^6 = 64

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

If omega is a complex cube root of unity, then show that: (a + b)^2 + (aomega + bomega^2)^2 + (aomega^2 + bomega)^2 = 6ab