Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.3 The Product and Quotient Theorems - 8.3 Exercises - Page 376: 34

Answer

$\frac{30(cos(\frac{2\pi}{5}) + isin(\frac{2\pi}{5}))}{10(cos(\frac{\pi}{7}) + isin(\frac{\pi}{7}))}$ = $2.0732 + 2.1684i$

Work Step by Step

$\frac{30(cos(\frac{2\pi}{5}) + isin(\frac{2\pi}{5}))}{10(cos(\frac{\pi}{7}) + isin(\frac{\pi}{7}))}$ = $3 \frac{cis(\frac{2\pi}{5})}{cis(\frac{\pi}{7})}$ = $3 cis(\frac{2\pi}{5} - \frac{\pi}{7})$ (Quotient Theorem) = $3 cis(\frac{9\pi}{35})$ = $2.0732 + 2.1684i$ (Using calculator and corr. to 4 decimal places)
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