Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - Chapter Test: 33

Answer

$\frac{4}{85}+\frac{33i}{85}$

Work Step by Step

$\frac{3+2i}{6-7i}$ =$\frac{3+2i}{6-7i}\times\frac{6+7i}{6+7i}$ =$\frac{(3+2i)(6+7i)}{6^{2}-(7i)^{2}}$ =$\frac{3(6+7i)+2i(6+7i)}{36-49i^{2}}$ =$\frac{18+21i+12i+14i^{2}}{36-49(-1)}$ =$\frac{18+33i-14}{85}$ =$\frac{4+33i}{85}$ =$\frac{4}{85}+\frac{33i}{85}$
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