Answer
$-\dfrac{2}{5}-\dfrac{3}{5}i$
Work Step by Step
Multiplying both the numerator and the denominator by the denominator of the given expression, $
\dfrac{3-2i}{5i}
,$ then
\begin{align*}\require{cancel}
&
\dfrac{3-2i}{5i}\cdot\dfrac{5i}{5i}
\\\\&=
\dfrac{3(5i)-2i(5i)}{5i(5i)}
\\\\&=
\dfrac{15i-10i^2}{25i^2}
\\\\&=
\dfrac{15i-10(-1)}{25(-1)}
&\text{ (use $i^2=-1$)}
\\\\&=
\dfrac{15i+10}{-25}
\\\\&=
-\dfrac{10+15i}{25}
\\\\&=
-\dfrac{\cancel{10}^2+\cancel{15}^3i}{\cancel{25}^5}
&\text{ (divide by $5$)}
\\\\&=
-\dfrac{2+3i}{5}
\\\\&=
-\dfrac{2}{5}-\dfrac{3}{5}i
.\end{align*}
Hence, the simplified form of the given expression is $
-\dfrac{2}{5}-\dfrac{3}{5}i
$.
