If `omega` is a complex cube root of unity, show that `frac{a+b omega+c omega^2}{c+a omega+b omega^2}` =`omega^2`

If omega is a complex cube root of unity, show that (2- omega )(2- omega^2 ) = 7

If omega is a complex cube root of unity, show that (a+b) + (a omega +b omega^2 )+(a omega^2 +b omega ) =0

If omega is of complex cube root of unity, then the value of [ frac{a+ b omega + c omega^2}{c+ a omega + b omega^2} + frac{a+ b omega + c omega^2}{b+ c omega + a omega^2} ] is

If omega is a complex cube root of unity, then show that: (a + bomega + comega^2) / (c + aomega + bomega^2) = omega^2

If omega is a complex cube root of unity, then show that: (1 + omega - omega^2)^6 = 64

If omega is a complex cube root of unity, then show that: (2 - omega) (2 - omega^2) = 7

If omega is a complex cube root of unity, show that (1+omega)^3 - (1+omega^2)^3 =0

If omega is a complex cube root of unity, show that (1+omega-omega^2)^6 = 64

If omega is a complex cube root of unity, show that (3+3 omega+5 omega^2)^6 - (2+6omega+2 omega^2)^3 =0

If omega is a complex cube root of unity, show that (a+b)^2 + (a omega+b omega^2)^2 +(a omega^2 +b omega)^2 =6ab