Question

Write the following in the form a+ib, where i =square root of -1:( square root of -27)(square root of 12)-(square root of -125)(square root of -5)

Answer 1

$$\begin{gathered} \sqrt{-27}\times \sqrt{12}-\sqrt{-125}\times \sqrt{-5} \\ =\sqrt{-27\times 12}-\sqrt{-125\times -5} \\ =\sqrt{-1\times 3\times 3\times 3\times 3\times 2\times 2}-\sqrt{5\times 5\times 5\times 5} \\ =18\sqrt{-1}-25 \\ =-25+18i \end{gathered}$$