(x+y)^(2)+(x omega+y omega^(2))^(2)+(x omega^(2)+y omega)^(2)=

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

Show that (x + omega y + omega^(2)z) (x + omega^(2)y + omega z) = x^(2) + y^(2) + z^(2)- yz - zx - xy

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

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) =

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 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

(x omega ^ (2) + y omega + z) / (x omega + y + omega ^ (2)) = ((x omega + y + z omega ^ (2)) / (x omega ^ (2) + and omega + z)) ^ (2)

If omega is a complex cube root of unity, then (x+y)^3+(x(omega)+y(omega)^2)^3+(x(omega)^2+y(omega))^3=

if omega!=1 is cube root of unity and x+y+z!=0(x)/(1+omega),(y)/(omega+omega^(2)),(z)/(omega^(2)+1)(y)/(omega+omega^(2)),(z)/(omega^(2)+1),(x)/(1+omega)(z)/(omega^(2)+1),(x)/(1+omega),(y)/(omega+omega^(2))]|=0 if

If x= a+ b, y = a omega + b omega^(2), z= a omega^(2) + b omega , then the value of x^(3) + y^(3) + z^(3) is equal to (where omega is imaginary cube root of unity)