Answer
$\frac{1}{3}-\frac{5}{3}i$.
Work Step by Step
The given expression is
$=\frac{5+i}{3i}$
Multiply the numerator and the denominator by $3i$.
$=\frac{5+i}{3i}\cdot \frac{3i}{3i}$
Use the distributive property in the numerator.
$=\frac{15i+3i^2}{9i^2}$
Use $i^2=-1$.
$=\frac{15i-3}{-9}$
Rewrite as $a+ib$.
$=\frac{-3}{-9}+\frac{15}{-9}i$
Simplify.
$=\frac{1}{3}-\frac{5}{3}i$.
