If `w` is cube roots of unity `x=a+b` , `y=a omega+b omega^(2)` `z=a omega^(2)+b omega` then find `x^(3)+y^(3)+z^(3)=?`

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

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

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

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

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

If x= a + b, y= a omega^(2) + b omega, z= a omega + b omega^(2) , then show that x^(3)+ y^(3) + z^(3)= 3(a^(3) + b^(3))

Show that x^(3) +y^(3) = (x + y) (omega x + omega^(2)y) (omega^(2)x + omega y)

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 omega is a complex cube root of unity, then (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)=

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