Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Quiz (Sections 8.1-8.4) - Page 379: 5c

Answer

The equivalent trigonometric form of $-3 - i$ is $\sqrt{10}cis198.435^\circ$ or $\sqrt{10}(cos198.435^\circ + isin198.435^\circ)$.

Work Step by Step

$-3 - i$ is at $arctan(\frac{-1}{-3})+180^\circ = 198.435^\circ$ with absolute value $\sqrt{(-3)^2 + (-1)^2} = \sqrt{10}$. The equivalent trigonometric form of $-3 - i$ is $\sqrt{10}cis198.435^\circ$ or $\sqrt{10}(cos198.435^\circ + isin198.435^\circ)$.
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