Question

Simplify the expression to a+bi form

Answer 1

$-\sqrt{100}-\sqrt{-192}+\sqrt4-\sqrt{-27}=(*)\\\\\sqrt{100}=10\ because\ 10^2=100\\\\\sqrt{-192}=\sqrt{-1}\cdot\sqrt{192}=i\sqrt{64\cdot3}=i\sqrt{64}\cdot\sqrt3=8i\sqrt3\\_{\sqrt{64}=8\ because\ 8^2=64,\ use\ \sqrt{-1}=i\ and\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}}\\\\\sqrt4=2\ because\ 2^2=4\\\\\sqrt{-27}=\sqrt{-1}\cdot\sqrt{27}=i\sqrt{9\cdot3}=i\sqrt9\cdot\sqrt3=3i\sqrt3\\_{\sqrt9=3\ because\ 3^2=9}\\\\(*)=-10-8i\sqrt3+2-3i\sqrt3=(-10+2)+(-8i\sqrt3-3i\sqrt3)\\\\=-8+(-11\sqrt3)i=-8-11\sqrt3i$