Answer
$\dfrac{3-2i}{2}$
Work Step by Step
Multiplying the numerator and the denominator by $i$, the expression $
\dfrac{2+3i}{2i}
$ simplifies to
\begin{array}{l}
\dfrac{2+3i}{2i}
\cdot
\dfrac{i}{i}
\\\\=
\dfrac{2i+3i^2}{2i^2}
\\\\=
\dfrac{2i+3(-1)}{2(-1)}
\\\\=
\dfrac{-3+2i}{-2}
\\\\=
-\dfrac{-3+2i}{2}
\\\\=
\dfrac{3-2i}{2}
.\end{array}
