Question

Express $(-\sqrt{3}+\sqrt{-2})(2\sqrt{3}-i)$ in the form (a+ib).

Answer 1

We have

$(-\sqrt{3}+\sqrt{-2})(2\sqrt{3}-i)=(-\sqrt{3}+i\sqrt{2})(2\sqrt{3}-i)$

$=-6+i\sqrt{3}+2\sqrt{6}i-\sqrt{2}{i}^2$

$=(-6+\sqrt{2})+\sqrt{3}(1+2\sqrt{2})i$.