Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 464: 110

Answer

$2-i\sqrt{2}$

Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ \dfrac{4-\sqrt{-8}}{2} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{4-\sqrt{-1}\cdot\sqrt{8}}{2} \\\\= \dfrac{4-i\cdot\sqrt{4\cdot2}}{2} \\\\= \dfrac{4-i\cdot\sqrt{(2)^2\cdot2}}{2} \\\\= \dfrac{4-2i\sqrt{2}}{2} \\\\= \dfrac{2(2-i\sqrt{2})}{2} \\\\= \dfrac{\cancel{2}(2-i\sqrt{2})}{\cancel{2}} \\\\= 2-i\sqrt{2} .\end{array}
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