Answer
$-\dfrac{5i+3}{4}$
Work Step by Step
Multiplying the denominator by $i$, the given expression, $
\dfrac{5-3i}{4i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5-3i}{4i}\cdot\dfrac{i}{i}
\\\\=
\dfrac{5(i)-3i(i)}{4i^2}
\\\\=
\dfrac{5i-3i^2}{4(-1)}
\\\\=
\dfrac{5i-3(-1)}{4(-1)}
\\\\=
\dfrac{5i+3}{-4}
\\\\=
-\dfrac{5i+3}{4}
.\end{array}
