Question

Simplify 9 divided by 3 minus 2i

Answer 1

$\dfrac{9}{3-2i}=\dfrac{9}{3-2i}\cdot\dfrac{3+2i}{3+2i}=\dfrac{9(3+2i)}{(3-2i)(3+2i)}\\\\\text{Use distributive property and}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{(9)(3)+(9)(2i)}{3^2-(2i)^2}=\dfrac{27+18i}{9-4i^2}=\dfrac{27+18i}{9-4(-1)}=\dfrac{27+18i}{9+4}\\\\=\boxed{\dfrac{27+18i}{13}}\to\boxed{D.}$