Let `\omega` be the imaginary cube root of 1. If `x=a+b`, `y=a\omega + b\omega^2`, `z = a\omega^2+b\omega`, then show that --
i) `xyz = a^3 + b^3`
ii) `x^3 + y^3 + z^3 = 3(a^3 + b^3)`
iii) `x^2 + y^2 + z^2 = 6ab`