# Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 73

$-\dfrac{5i+3}{4}$

#### 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}

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