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 314: 12

Answer

The standard form of the expression $\left( -4-8i \right)\left( 3+i \right)$ is $-4-28i$.

Work Step by Step

Consider the expression $\left( -4-8i \right)\left( 3+i \right)$. Use the FOIL method. $\left( -4-8i \right)\left( 3+i \right)=-12-4i-24i-8{{i}^{2}}$ Replace the value ${{i}^{2}}=-1$. $\left( -4-8i \right)\left( 3+i \right)=-12-4i-24i-8\left( -1 \right)$ Make a group of real and imaginary terms. $\left( -4-8i \right)\left( 3+i \right)=-12+8-4i-24i$ Simplify the real and imaginary terms. $\begin{align} & \left( -4-8i \right)\left( 3+i \right)=\left( -12+8 \right)+\left( -4-24 \right)i \\ & =-4-28i \end{align}$ Therefore, the standard form of the expression $\left( -4-8i \right)\left( 3+i \right)$ is $-4-28i$.
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