Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX H - Complex Numbers - H Exercises: 26

Answer

$2(cos(\frac{5\pi}{3})+isin(\frac{5\pi}{3}))$

Work Step by Step

First calculate the modulus of the complex number with the rule $|z|=\sqrt{x^2 + y^2}$, so $\sqrt{1^2 + (-\sqrt{3})^2} = 2 $. Thereafter determine the angle between the line and the positive x-axis in counter-clockwise direction. The real part (x-axis) is positive and the imaginary part (y-axis) is negative and $sin(\theta)=-\sqrt{3}$ so $\theta = \frac{5\pi}{3}$.
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