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$\newcommand{\multiplyright}[2][\cdot]{{\color{blue}{{{}#1#2}}}}\newcommand{\amp}{&}$

Rationalize the denominator in the expression $\frac{5}{3i}\text{.}$

Solution

$\begin{aligned} \frac{5}{3i}\amp=\frac{5\multiplyright{i}}{3i\multiplyright{i}}\\ \amp=\frac{5i}{3(-1)}\\ \amp=-\frac{5i}{3}\\ \amp=-\frac{5}{3}i \end{aligned}$