Question

Multiply $x-\frac{1+\sqrt{-3}}{2}$ by $x-\frac{1-\sqrt{-3}}{2}$

Answer 1

We have $(x-\frac{1+\sqrt{-3}}{2})\times (x-\frac{1-\sqrt{-3}}{2})$

$=(x-\omega )(x-{\omega }^2)$

$=x^2-(\omega +{\omega }^2)x+{\omega }^3$

$=x^2+x+1$