The value of `(x+y)(omegax+omega^2y)(omega^2x+omegay)` is
(a) `x+omega+omega^2` (b) `x+y` (a) `xomega+y` (a) `x^3+y^3`

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

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

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

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

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

Find x + y + z + w

If 1,x_(1),x_(2),x_(3) are the roots of x^(4)-1=0andomega is a complex cube root of unity, find the value of ((omega^(2)-x_(1))(omega^(2)-x_(2))(omega^(2)-x_(3)))/((omega-x_(1))(omega-x_(2))(omega-x_(3)))