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 - Chapter Review - Review Exercises - Page 655: 21

Answer

$z\cdot w=5(cos5^\circ+i\ sin5^\circ)$, $\frac{z}{w}=5(cos15^\circ+i\ sin15^\circ)$

Work Step by Step

1. Use the given numbers, we have $z\cdot w=5(cos(10+355)^\circ+i\ sin(10+355)^\circ)=5(cos365^\circ+i\ sin365^\circ)=5(cos5^\circ+i\ sin5^\circ)$ 2. we have $\frac{z}{w}=5(cos(10-355)^\circ+i\ sin(10-355)^\circ)=5(cos(-345)^\circ+i\ sin(-345)^\circ)=5(cos15^\circ+i\ sin15^\circ)$
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