Question

The value of $\frac{-1+\sqrt{3}i}{2}+\frac{-1-\sqrt{3}i}{2}$ is

Answer 1

We know that

$\left(\frac{-1+\sqrt{3}i}{2}\right)=\omega$

Hence,

$\left(\frac{-1-\sqrt{3}i}{2}\right)={\omega }^2$

Now,

$\left(\frac{-1+\sqrt{3}i}{2}\right)+\left(\frac{-1-\sqrt{3}i}{2}\right)=\omega +{\omega }^2$

And,

$1+\omega +{\omega }^2=0$

Hence,

$\omega +{\omega }^2=-1$

Therefore,

correct answer is $-1$