#### Answer

$\dfrac{6-17i}{25}$

#### Work Step by Step

Multiplying by the conjugate of the denominator, the given expression, $
\dfrac{3-2i}{4+3i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{3-2i}{4+3i}\cdot\dfrac{4-3i}{4-3i}
\\\\=
\dfrac{3(4)+3(-3i)-2i(4)-2i(-3i)}{(4)^2-(3i)^2}
\\\\=
\dfrac{12-9i-8i+6i^2}{16-9i^2}
\\\\=
\dfrac{12-9i-8i+6(-1)}{16-9(-1)}
\\\\=
\dfrac{12-9i-8i-6}{16+9}
\\\\=
\dfrac{(12-6)+(-9i-8i)}{16+9}
\\\\=
\dfrac{6-17i}{25}
\end{array}