Prove that
`(3+3 omega+5 omega^2)^6 = (3+5omega+3 omega^2)^6 = 64`

omega is an imaginary root of unity.Prove that (a+b omega+c omega^(2))^(3)+(a+b omega^(2)+c omega)^(3)=(2a-b-c)(2b-a-c)(2c-a-b)

If omega,omega^(2) be imaginary cube root of unity then (3+3 omega+5 omega^(2))^(6)-(2+6 omega+2 omega^(2))^(3) is equal to

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

(2 + omega + omega ^ (2)) ^ (3) + (1 + omega-omega ^ (2)) ^ (3) = (1-3 omega + omega ^ (2)) ^ (4) = 1

If omega is complex cube root of unity then (3+5 omega+3 omega^(2))^(2)+(3+3 omega+5 omega^(2))^(2) is equal to

If omega is complex cube root of unity then (3+5 omega+3 omega^(2))^(2)+(3+3 omega+5 omega^(2))^(2) is equal to

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