Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 570: 75

Answer

$\frac{11}{13}-\frac{16}{13}i$.

Work Step by Step

The given expression is $=\frac{5-2i}{3+2i}$ The conjugate of the denominator is $3-2i$. Multiply the numerator and the denominator by $3-2i$. $=\frac{5-2i}{3+2i}\cdot \frac{3-2i}{3-2i}$ $=\frac{15-10i-6i+4i^2}{3^2-(2i)^2}$ Use $i^2=-1$. $=\frac{15-10i-6i-4}{9+4}$ Simplify. $=\frac{11-16i}{13}$ Rewrite as $a+ib$. $=\frac{11}{13}-\frac{16}{13}i$.
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