Answer
$\dfrac{7-2i}{5}$
Work Step by Step
Multiplying the denominator by $i$, the given expression, $
\dfrac{2+7i}{5i}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{2+7i}{5i}\cdot\dfrac{i}{i}
\\\\=
\dfrac{2(i)+7i(i)}{5i^2}
\\\\=
\dfrac{2i+7i^2}{5i^2}
\\\\=
\dfrac{2i+7(-1)}{5(-1)}
\\\\=
\dfrac{2i-7}{-5}
\\\\=
-\dfrac{2i-7}{5}
\\\\=
\dfrac{7-2i}{5}
.\end{array}
