Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Appendix G - Exercises - Page A12: 30

Answer

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