Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.1 - Complex Numbers - 8.1 Problem Set - Page 427: 106


(c) $\frac{14}{25}+\frac{23}{25}i$

Work Step by Step

$\frac{5+2i}{4-3i}$ =$\frac{5+2i}{4-3i}\times\frac{4+3i}{4+3i}$ =$\frac{5(4+3i)+2i(4+3i)}{4^{2}-(3i)^{2}}$ =$\frac{20+15i+8i+6i^{2}}{16-9i^{2}}$ =$\frac{20+15i+8i+6(-1)}{16-9(-1)}$ =$\frac{14+23i}{25}$ =$\frac{14}{25}+\frac{23}{25}i$
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