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: 58

Answer

The equivalent trigonometric form of $11 + 2i$ is $11.18cis10.30^\circ$ or $11.18(cos10.30^\circ + isin10.30^\circ)$.

Work Step by Step

For $11 + 2i$, the absolute value is $\sqrt{11^2 + 2^2} = 11.18$ and $\theta = arctan(\frac{2}{11}) = 10.30^\circ$, since $11 + 2i$ is in the 1st quadrant. Therefore, the equivalent trigonometric form of $11 + 2i$ is $11.18cis10.30^\circ$ or $11.18(cos10.30^\circ + isin10.30^\circ)$.
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