If `w` is cube roots unity then prove that `a+b+a(w+w^2)+b(w+w^2) =0`

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 1+omega = …..

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

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

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

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

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]