[tex]\text{ }\frac{-4\text{ - 2i }}{\text{ 3 + 2i}}[/tex]
Let's apply the Complex Arithmetic Rule:
[tex]\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}\:=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}[/tex]
We have: a = -4, b = -2, c = 3 & d = 2
[tex]\frac{\left(-4\cdot \:3+\left(-2\right)\cdot \:2\right)+\left(-2\cdot \:3-\left(-4\right)\cdot \:2\right)i}{3^2+2^2}[/tex][tex]\frac{(-12\text{ - 4\rparen + \lparen-6 + 8\rparen i}}{9\text{ + 4}}[/tex][tex]\frac{-16+2i}{13}[/tex]
