If `omega` is the complex cube of unity, find the value of `(1-omega- omega^2)^3` + `(1-omega+omega^2)^3`

If omega is the complex cube of unity, find the value of (1+ omega^2)^3

If omega is the complex cube of unity, find the value of omega + frac{1}{omega}

If omega is the complex cube of unity, find the value of omega^2 + omega^3 + omega^4

If omega is the complex cube of unity, find the value of (1+ omega )(1+ omega^2 ) (1+ omega^4 )(1+ omega^8 )

If omega is a complex cube root of unity, then find the values of: (1 + omega^2)^3

If omega is a complex cube root of unity, then find the values of: (1 - omega - omega^2)^3 + (1 - omega + omega^2)^3

If omega is a complex cube root of unity, then find the values of: omega + 1/omega

If omega is a complex cube root of unity, then find the values of: omega^2 + omega^3 + omega^4

If omega is a complex cube root of unity, then find the values of: (1 + omega) (1 + omega^2) (1 + omega^4) (1 + omega^8)