Trigonometry 7th Edition

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

Chapter 8 - Section 8.2 - Trigonometric Form for Complex Numbers - 8.2 Problem Set - Page 433: 60

Answer

The equivalent trigonometric form of $-8 - 15i$ is $17cis241.93^\circ$ or $17(cos241.93^\circ + isin241.93^\circ)$.

Work Step by Step

For $-8 - 15i$, the absolute value is $\sqrt{(-8)^2 + (-15)^2} = 17$ and $\theta = arctan(\frac{-15}{-8}) = 241.93^\circ$, since $-8 - 15i$ is in the 3rd quadrant. Therefore, the equivalent trigonometric form of $-8 - 15i$ is $17cis241.93^\circ$ or $17(cos241.93^\circ + isin241.93^\circ)$.
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