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

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 omega + omega^(2)= …..

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 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 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)]

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)]

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

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