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: 54

Answer

The equivalent trigonometric form of $3 + 4i$ is $5cis53.13^\circ$ or $5(cos53.13^\circ + isin53.13^\circ)$.

Work Step by Step

For $3 + 4i$, the absolute value is $\sqrt{3^2 + 4^2} = 5$ and $\theta = arctan(\frac{4}{3}) = 53.13^\circ$, since $3 + 4i$ is in the 1st quadrant. Therefore, the equivalent trigonometric form of $3 + 4i$ is $5cis53.13^\circ$ or $5(cos53.13^\circ + isin53.13^\circ)$.
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