Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.3 The Complex Plane; De Moivre's Theorem - 8.3 Assess Your Understanding - Page 615: 38

Answer

$zw=8(cos\frac{15\pi}{16}+i\ sin\frac{15\pi}{16}), \frac{z}{w}= 2(cos\frac{29\pi}{16}+i\ sin\frac{29\pi}{16})$

Work Step by Step

Given $z=4(cos\frac{3\pi}{8}+i\ sin\frac{3\pi}{8})$ and $w=2(cos\frac{9\pi}{16}+i\ sin\frac{9\pi}{16})$, we have: 1. $zw=8(cos(\frac{3\pi}{8}+\frac{9\pi}{16})+i\ sin(\frac{3\pi}{8}+\frac{9\pi}{16}))=8(cos\frac{15\pi}{16}+i\ sin\frac{15\pi}{16})$ 2. $\frac{z}{w}=2(cos(\frac{3\pi}{8}-\frac{9\pi}{16})+i\ sin(\frac{3\pi}{8}-\frac{9\pi}{16}))=2(cos\frac{-3\pi}{16}+i\ sin\frac{-3\pi}{16})=2(cos\frac{29\pi}{16}+i\ sin\frac{29\pi}{16})$
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