If `omega` is non-real cube roots of unity, then prove that `|(x+yomega+zomega^2)/(x w+z+yomega^2)|=1`

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 non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

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

If omega is a non real cube root of unity then (a+b)(a+b omega)(a+b omega^(2)) is

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

If omega is a non real cube root of unity, then (a+b)(a+b(omega))(a+b(omega)^2) is

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 prove that (2 - omega)(2 -omega^(2)) (2 - omega^(10)) ( 2 - omega^(11)) = 49 .

If i=sqrt(-1) and omega is a non-real cube root of unity,then the value of omega-omega^(2)quad 1+iquad omega^(2) is

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