## Calculus 8th Edition

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