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: 56

Answer

The equivalent trigonometric form of $-21 - 20i$ is $29cis223.60^\circ$ or $29(cos223.60^\circ + isin223.60^\circ)$.

Work Step by Step

For $-21 - 20i$, the absolute value is $\sqrt{(-21)^2 + (-20)^2} = 29$ and $\theta = arctan(\frac{-20}{-21}) = 223.60^\circ$, since $-21 - 20i$ is in the 3rd quadrant. Therefore, the equivalent trigonometric form of $-21 - 20i$ is $29cis223.60^\circ$ or $29(cos223.60^\circ + isin223.60^\circ)$.
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