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 571: 139

Answer

False.

Work Step by Step

The given expression is $=\frac{7+3i}{5+3i}$ The conjugate of the denominator is $5-3i$. Multiply the numerator and the denominator by $5-3i$. $=\frac{7+3i}{5+3i}\cdot \frac{5-3i}{5-3i}$ Use the special formula $(A+B)^2=A^2+2AB+B^2$ $=\frac{35-21i+15i-9i^2}{5^2-(3i)^2}$ Use $i^2=-1$. $=\frac{35-21i+15i+9}{25+9}$ Simplify. $=\frac{44-6i}{34}$ Rewrite as $a+ib$. $=\frac{44}{34}-\frac{6}{34}i$ Simplify. $=\frac{22}{17}-\frac{3}{17}i$. Hence, the given statement is false.
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