Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.1 - Complex Numbers - Exercise Set - Page 315: 55


The standard form of the expression $5\sqrt{-16}+3\sqrt{-81}$ is $0+47i$.

Work Step by Step

Consider the expression,$5\sqrt{-16}+3\sqrt{-81}$ Express all the square roots of negative numbers in terms of $i$. $5\sqrt{-16}+3\sqrt{-81}=5i\sqrt{16}+3i\sqrt{81}$ Simplify the radicals. $\begin{align} & 5\sqrt{-16}+3\sqrt{-81}=5i\sqrt{{{4}^{2}}}+3i\sqrt{{{9}^{2}}} \\ & =5i\left( 4 \right)+3i\left( 9 \right) \\ & =20i+27i \\ & =47i \end{align}$ Express the complex number in the standard form. $5\sqrt{-16}+3\sqrt{-81}=0+47i$ Therefore, the standard form of the expression $5\sqrt{-16}+3\sqrt{-81}$ is $0+47i$.
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