If `w` is cube roots of unity then prove that, `(a+b) (aw+bw^2) (aw^2+bw) = (a^3 +b^3)`

If omega is a cube root of unity, then 1+omega = …..

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then 1+ omega^(2)= …..

If w is a complex cube root of unity then show that ( 2 − w ) ( 2 − w^2 ) ( 2 − w^10 ) ( 2 − w^11 ) = 49 ?

If omega is a cube root of unity, then omega + omega^(2)= …..

If 1, omega, omega^(2) are the cube roots of unity, prove that (x-y) (x omega-y) (x omega^(2)-y)= x^(3)-y^(3)

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 1, omega and omega^(2) are the cube roots of unity, prove that (a+b omega+c omega^(2))/(c+a omega+b omega^(2))=omega^(2)

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega^(2))^(4)= omega