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: 13

Answer

The standard form of the expression $\left( 7-5i \right)\left( -2-3i \right)$ is $-29-11i$.

Work Step by Step

Consider the expression $\left( 7-5i \right)\left( -2-3i \right)$. Use the FOIL method. $\left( 7-5i \right)\left( -2-3i \right)=-14-21i+10i+15{{i}^{2}}$ Replace the value ${{i}^{2}}=-1$. $\left( 7-5i \right)\left( -2-3i \right)=-14-21i+10i+15\left( -1 \right)$ Make a group of real and imaginary terms. \[\left( 7-5i \right)\left( -2-3i \right)=-14-15+10i-21i\] Simplify the real and imaginary terms. \[\begin{align} & \left( 7-5i \right)\left( -2-3i \right)=\left( -14-15 \right)+\left( 10-21 \right)i \\ & =-29-11i \end{align}\] Therefore, the standard form of the expression $\left( 7-5i \right)\left( -2-3i \right)$ is $-29-11i$.
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