Question

If α and β are the complex cube roots of unity, then find α2+β2+αβ.

Answer 1

cube roots of unity is 1, w, w^2....(read "w" as omega)..
so
$\alpha$
= w..
$\beta$
= w^2....

so,

alpha ^2 = w^2...
beta^2 = w^4=w...
alpha*beta= w^3=1
so, the ans is, 1+w+w^2=0