Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set: 24

Answer

$2i+2i\sqrt{3}$

Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ \sqrt{-4}+\sqrt{-12} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{4}\cdot\sqrt{-1}+\sqrt{12}\cdot\sqrt{-1} \\\\= \sqrt{4}\cdot i+\sqrt{4\cdot3}\cdot i \\\\= \sqrt{(2)^2}\cdot i+\sqrt{(2)^2\cdot3}\cdot i \\\\= 2i+2i\sqrt{3} .\end{array}
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