Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 67

$\dfrac{6+4i}{13}$

Multiplying by the conjugate of the denominator, the given expression, $ \dfrac{2}{3-2i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{2}{3-2i}\cdot\dfrac{3+2i}{3+2i} \\\\= \dfrac{2(3)+2(2i)}{(3)^2-(2i)^2} \\\\= \dfrac{6+4i}{9-4i^2} \\\\= \dfrac{6+4i}{9-4(-1)} \\\\= \dfrac{6+4i}{9+4} \\\\= \dfrac{6+4i}{13} .\end{array}