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: 57

Answer

The equivalent trigonometric form of $7 - 24i$ is $25cis286.26^\circ$ or $25(cos286.26^\circ + isin286.26^\circ)$.

Work Step by Step

For $7 - 24i$, the absolute value is $\sqrt{7^2 + (-24)^2} = 25$ and $\theta = arctan(\frac{-24}{7}) = 286.26^\circ$, since $7 - 24i$ is in the 4th quadrant. Therefore, the equivalent trigonometric form of $7 - 24i$ is $25cis286.26^\circ$ or $25(cos286.26^\circ + isin286.26^\circ)$.
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