If `1 , omega , omega^(2)` are the cube roots of unity, then prove that
`( x + y + z) ( x + y omega + z omega^(2)) ( x + yomega^(2) + z omega) = x^(3) + y^(3) + z^(3) - 3xyz`

If 1 , omega , omega^(2) are the cube roots of unity , then (x + y + z) (z + y omega + zomega^(2)) ( x + y omega^(2) + z omega) =

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 omega is non-real cube roots of unity,then prove that |(x+y omega+z omega^(2))/(xw+z+y omega^(2))|=1

If omega is a complex cube roots of unity then show that following. (x - y) (xomega - yomega^2) (xomega^2 - yomega) = x^3 - y^3

Prove that (x+y+z)(x+omega y+omega^(2)z)(x+omega^(2)y+omega z)=x^(3)+y^(3)+z^(3)-3xyz

If omega be an imaginary cube root or unity, prove that (x+y omega+ z omega^(2))^(4)+ (x omega+ y omega^(2)+z)^(4)+(x omega^(2)+y+ z omega)^(4)=0

If 1,omega,omega^2 are the cube roots of unity then prove the following i) (1-omega+omega^2) + (1+omega-omega^2)^5=32 ii) (x+y+z)(x+yomega+zomega^2)(x+yomega^2+zomega)=x^3+y^3+z^3-3xyz

If x=a+b, y=a omega+b omega^(2), z=a omega^(2)+b omega , then x y z=

If omega is an imaginary cube root of unity then prove that (xomega^2+yomega+z)/(xomega+y+zomega^2)=((xomega+y+zomega^2)/(xomega^2+yomega+z))^2