Calculus 8th Edition

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

Appendix G - Complex Numbers - G Exercises - Page A56: 30


a) $64 [\cos (7\pi/3)+i \sin (7\pi/3)]$ b) $\cos (4\pi/3)+i \sin (4\pi/3)$ c) $\dfrac{1}{8}[\cos (-11\pi/6)+i \sin (-11\pi/6)]$

Work Step by Step

Here, $z=8 [\cos (\dfrac{11\pi}{6})+i \sin (\dfrac{11\pi}{6})]$ and $w=8 [\cos (\pi/2)+i \sin (\pi/2)]=64 [\cos (\dfrac{7\pi}{3})+i \sin (7\pi/3)]$ a) $zw=8 [\cos (\dfrac{11\pi}{6})+i \sin (\dfrac{11\pi}{6})] \times 8 [\cos (\pi/2)+i \sin (\pi/2)]=64 [\cos (\dfrac{7\pi}{3})+i \sin (\dfrac{7\pi}{3})]$ b) $\dfrac{z}{w}=\dfrac{8 [\cos (\dfrac{11\pi}{6})+i \sin (\dfrac{11\pi}{6})]}{8 [\cos (\pi/2)+i \sin (\pi/2)]}=\cos (\dfrac{4\pi}{3})+i \sin (\dfrac{4\pi}{3})$ c) $\dfrac{1}{z}=\dfrac{1}{8 [\cos (\dfrac{11\pi}{6})+i \sin (11(\dfrac{11\pi}{6})]}=\dfrac{1}{8}[\cos(-\dfrac{11\pi}{6})+i \sin (-\dfrac{11\pi}{6})]$
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