If `omega` be imaginary cube root of 1 , then prove that
`(xomega^(2)+yomega+z)/(xomega+y+zomega^(2))=((xomega+y+zomega^(2))/(xomega^(2)+yomega+z))^(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 be an imaginary cube root of unity, show that (xomega^(2)+yomega+z)/(xomega+y+zomega^(2))=omega

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 omega be an imaginaryb cube root of unity,then prove that, 1/(1+2omega)+1/(2+omega)-1/(1+omega)=0

If omega be an imaginary cube root of unity, show that (x+yomega+zomega^(2))^(2)+(xomega+yomega^(2)+z)^(2)+(xomega^(2)+y+zomega)^(2)=0

If omega be an imaginary cube root of unity, show that, (1-omega)(1-omega^(2))(1-omega^(4))(1-omega^(5))=9

If omega be an imaginary cube root or unity, prove that (1)/(1+2 omega)-(1)/(1+ omega)+(1)/(2+omega)=0

If omega be an imaginary cube root of unity, show that (1+omega-omega^(2))(1-omega+omega^(2))=4

If omega is an imaginary cube root of unity, then the value of (1+ omega- omega^(2))(1- omega + omega ^(2)) is-

If omega is an imaginary cube root of unity, then the value of the determinant |(1+omega,omega^(2),-omega),(1+omega^(2),omega,-omega^(2)),(omega+omega^(2),omega,-omega^(2))| is