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

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

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 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: (2 - omega) (2 - omega^2) = 7

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: (3 + 3omega + 5omega^2)^6 - (2 + 6omega + 2omega^2)^3 = 0

If omega is a complex cube roots of unity then show that following. (a + b)^3 + (aomega + bomega^2)^3 + (aomega^2 + bomega)^3 = 3(a^3 + b^3)

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

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