Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.4 - Imaginary Numbers as Solutions of Quadratic Equations - Exercise Set: 11

Answer

$7+4i$

Work Step by Step

Using the properties of radicals and that $i=\sqrt{-1}$, then the given expression, $ 7+\sqrt{-16} ,$ is equivalent to \begin{array}{l}\require{cancel} 7+\sqrt{-1}\cdot\sqrt{16} \\\\= 7+i\cdot\sqrt{(4)^2} \\\\= 7+i\cdot4 \\\\= 7+4i .\end{array}
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