If `w` are cube roots of unity then prove that, `w^4 + 2w^6 +w^8 =1`

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^(3) = ……

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

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

If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2, 1],[w^2, 1,w]|=0 .

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

If 1, omega, omega^(2) are three cube roots of unity, prove that omega^(28) + omega^(29) + 1= 0

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

If omega and omega^(2) are cube roots of unity, prove that (2- omega + 2omega^(2)) (2 + 2omega- omega^(2))= 9

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