`(a + b)^2 + ( aomega + bomega^2)^2 + (aomega^2 + bomega)^2 = `

If omega is a complex cube roots of unity then show that following. (a + 2b)^2 + (aomega + 2bomega^2)^2 +(aomega^2 + 2bomega)^2 = 12ab

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, then show that: (a + b) + (aomega + bomega^2) + (aomega^2 + bomega) = 0

If 1 , omega , omega^(2) are the cube roots of unity prove that (a + b) ( a omega + b omega^(2))(aomega^(2) + b omega) = a^(3) + b^(3)

(a-b)(aomega-bomega^(2))(aomega^(2)-bomega)

(a+2b)^(2)+(aomega+2bomega^(2))^(2)+(aomega^(2)+2bomega)^(2)

If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega , show that (i) xyz = a^3 + b^3

Prove that a^3 + b^3 + c^3 – 3abc = (a + b + c) (a + bomega + comega^2) (a + bomega^2 + "c"omega) , where omega is an imaginary cube root of unity.

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