Question

Simplify the expression to a+bi form

Answer 1

`-√(100)-√(-192)+\sqrt4-√(-27)=(*)\\\\√(100)=10\ because\ 10^2=100\\\\√(-192)=√(-1)\cdot√(192)=i√(64\cdot3)=i√(64)\cdot\sqrt3=8i\sqrt3\\_(√(64)=8\ because\ 8^2=64,\ use\ √(-1)=i\ and\ √(ab)=√(a)\cdot√(b))\\\\\sqrt4=2\ because\ 2^2=4\\\\√(-27)=√(-1)\cdot√(27)=i√(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`