Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix G - Complex Numbers - G Exercises: 26

Answer

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

Work Step by Step

We are given: $z=1-\sqrt{3}i$ To find $r$ of a complex number $a+bi$, we use: $\sqrt{a^2+b^2}$: $r=\sqrt{1^{2}+(-\sqrt{3})^{2}}=2$ To find $\theta$, we use $\tan{\theta}=\frac{b}{a}$: $\displaystyle \tan\theta=\frac{-\sqrt{3}}{1}=-\sqrt{3}$ And since $z$ is in the 4th quadrant, we have: $\displaystyle \theta=\frac{5\pi}{3}$ To put the number in polar form, we use $r(\cos{\theta}+i\sin{\theta})$: $2(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3})$
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