Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-8 Complex Numbers - Practice and Problem-Solving Exercises - Page 253: 24

Answer

$9-23i$

Work Step by Step

Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method, the given expression, $ (-6-5i)(1+3i) ,$ is equivalent to \begin{align*} & -6(1)-6(3i)-5i(1)-5i(3i) \\&= -6-18i-5i-15i^2 \\&= -6-18i-5i-15(-1) &\text{ (use $i^2=-1$)} \\&= -6-18i-5i+15 .\end{align*} Combining the real parts and the imaginary parts, the expression above is equivalent to \begin{align*} & (-6+15)+(-18i-5i) \\&= 9+(-23i) \\&= 9-23i .\end{align*} Hence, the simplified form of the given expression is $ 9-23i $.
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