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: 53

Answer

The equivalent trigonometric form of $3 - 4i$ is $5cis306.87^\circ$ or $5(cos306.87^\circ + isin306.87^\circ)$.

Work Step by Step

For $3 - 4i$, the absolute value is $\sqrt{3^2 + (-4)^2} = 5$ and $\theta = arctan(\frac{-4}{3}) = 306.87^\circ$, since $3 - 4i$ is in the 4th quadrant. Therefore, the equivalent trigonometric form of $3 - 4i$ is $5cis306.87^\circ$ or $5(cos306.87^\circ + isin306.87^\circ)$.
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