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: 77



Work Step by Step

The given expression is $=\frac{4+5i}{3-7i}$ The conjugate of the denominator is $3+7i$. Multiply the numerator and the denominator by $3+7i$. $=\frac{4+5i}{3-7i}\cdot \frac{3+7i}{3+7i}$ $=\frac{12+28i+15i+35i^2}{3^2-(7i)^2}$ Use $i^2=-1$. $=\frac{12+28i+15i-35}{9+49}$ Simplify. $=\frac{-23+43i}{58}$ Rewrite as $a+ib$. $=-\frac{23}{58}+\frac{43}{58}i$.
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