` ( 1 + omega - omega ^ 2) ^6 = `

(2 + 5 omega + 2 omega ^ (2)) ^ (6) = (2 + 2 omega + 5 omega ^ (2)) ^ (6) = 729

If omega is a cube root of unity , then |{:( 1 , omega , 2 omega^(2)) , (2 , 2omega^(2) , 4 omega^(3)) , (3 , 3 omega^(3) , 6 omega^(4)):}| =

Prove the following (1- omega + omega^(2)) (1 + omega- omega^(2)) (1 - omega- omega^(2))= 8

If 1, omega, omega^(2) are three cube roots of unity, prove that (3+ 5omega + 3omega^(2))^(6) = (3 + 5omega^(2) + 3omega)^(6)= 64

If omega is a cube root of unity (1-2 omega+omega^(2))^(6)=

(1 + omega) (1 + omega^(2)) (1 + omega^(3)) (1 + omega^(4)) (1 + omega^(5)) (1 + omega^(6)) …. (1 + omega^(3n)) =

If 1, omega, omega^(2) are cube roots of unity, prove that (x + y)^(2) + (x omega + y omega^(2))^(2) + (x omega^(2) + y omega)^(2)= 6xy