Mathematics, 18.07.2019 05:30 ZoomZoom44
Use demoivre's theorem to find (4cis (pi/18))^3 a) 32+32root3i b) 32root3 + 32i c) 6+6root3i d) 6root3 +6i
Answers: 1
![\bf \qquad \textit{power of two complex numbers} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)]\\\\ -------------------------------](/tpl/images/0102/8970/d1c6f.png)
![\bf 4\left[ cos\left( \frac{\pi }{18} \right)+i~sin\left( \frac{\pi }{18} \right) \right]^3\implies 4^3\left[ cos\left(3\cdot \frac{\pi }{18} \right)+i~sin\left( 3\cdot \frac{\pi }{18} \right) \right] \\\\\\ 64\left[ cos\left( \frac{\pi }{6} \right)+i~sin\left( \frac{\pi }{6} \right) \right]\implies 64\left[\frac{\sqrt{3}}{2}+i~\frac{1}{2} \right] \\\\\\ 32\sqrt{3}+32i](/tpl/images/0102/8970/08091.png)
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Use demoivre's theorem to find (4cis (pi/18))^3 a) 32+32root3i b) 32root3 + 32i c) 6+6root3i d) 6roo...
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