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: 112

Answer

$\dfrac{1+i\sqrt{2}}{2}$

Work Step by Step

Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ \dfrac{7+\sqrt{-98}}{14} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{7+\sqrt{-1}\cdot\sqrt{98}}{14} \\\\= \dfrac{7+i\cdot\sqrt{49\cdot2}}{14} \\\\= \dfrac{7+i\cdot\sqrt{(7)^2\cdot2}}{14} \\\\= \dfrac{7+i\cdot7\sqrt{2}}{14} \\\\= \dfrac{7+7i\sqrt{2}}{14} \\\\= \dfrac{7(1+i\sqrt{2})}{14} \\\\= \dfrac{\cancel{7}(1+i\sqrt{2})}{\cancel{7}\cdot2} \\\\= \dfrac{1+i\sqrt{2}}{2} .\end{array}
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