Question
If α and β are the complex cube roots of unity, show that
1.$\alpha^2+\beta^2+\alpha \beta=0$
(ii) $\alpha^4+\beta^4+\alpha^{-1} \beta^{-1}=0$
2.If x = a + b, y = αa + βb and z = aβ + bα, where α and β are complex cube roots of unity,
show that $x y z=a^3+b^3$.