Question

Find the value of ${(-1+\sqrt{-3})}^2+{(-1-\sqrt{-3})}^2$.

Answer 1

$\begin{array}{c}{\left(-1+\sqrt{-3}\right)}^2+{\left(-1-\sqrt{-3}\right)}^2\\ ={\left(-1\right)}^2+{\left(\sqrt{3}\right)}^2+2\left(-1\right)\left(\sqrt{3}\right)+{\left(-1\right)}^2+{\left(-\sqrt{3}\right)}^2\\ =1-3-2\sqrt{3}+1-3+2\sqrt{-3}\\ =2-6\\ =-4\end{array}$