Question

Show If a= $\frac{-1+\sqrt{3}i}{2},b=\frac{-1-\sqrt{3}i}{2},$ then

$a+b=-1$

Answer 1

We have,

$a=\frac{-1+\sqrt{3}i}{2}$

$b=\frac{-1-\sqrt{3}i}{2}$

Now,

$a+b=\frac{-1+\sqrt{3}i}{2}+\frac{-1-\sqrt{3}i}{2}$

$a+b=\frac{-1+\sqrt{3}i-1-\sqrt{3}i}{2}$

$a+b=\frac{-1-1}{2}$

$a+b=-1$

Hence, this is the answer.