# Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 70

$\dfrac{3+6i}{10}$

#### Work Step by Step

Multiplying by the conjugate of the denominator, the given expression, $\dfrac{3i}{4+2i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{3i}{4+2i}\cdot\dfrac{4-2i}{4-2i} \\\\= \dfrac{3i(4)+3i(-2i)}{4^2-(2i)^2} \\\\= \dfrac{12i-6i^2}{16-4i^2} \\\\= \dfrac{12i-6(-1)}{16-4(-1)} \\\\= \dfrac{12i+6}{16+4} \\\\= \dfrac{6+12i}{20} \\\\= \dfrac{\cancel{2}(3+6i)}{\cancel{2}\cdot10} \\\\= \dfrac{3+6i}{10} .\end{array}

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