Question

Multiply $2\sqrt{-3}+3\sqrt{-2}$ by $4\sqrt{-3}-5\sqrt{-2}$

Answer 1

$(2\sqrt{-3}+3\sqrt{-2})\times (4\sqrt{-3}-5\sqrt{-2})$

$=(2\sqrt{3}\text{i}+3\sqrt{2}\text{i})\times (4\sqrt{3}\text{i}-5\sqrt{2}\text{i})$

$=-(2\sqrt{3}+3\sqrt{2})\times (4\sqrt{3}-5\sqrt{2})$

$=-(24-10\sqrt{6}+12\sqrt{6}-30)$

$=6-2\sqrt{6}$