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Question Number 48982 by peter frank last updated on 30/Nov/18

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Dec/18

$$2)\frac{\sqrt{3}}{2}=sin\left(\frac{\pi }{6}\right)\frac{1}{2}=cos\left(\frac{\pi }{6}\right)$$$$e^{i\theta }=cos\theta +isin\theta \leftarrow demoiverstheorem$$$$e^{-i\theta }=cos\theta -isin\theta$$$$z={\left(e^{i\frac{\pi }{6}}\right)}^{107}+{\left(e^{i\frac{-\pi }{6}}\right)}^{107}$$$$=e^{i\frac{107\pi }{6}}+e^{-i\frac{107\pi }{6}}$$$$=(cos\frac{107\pi }{6}+isin\frac{107\pi }{6})+(cos\frac{107\pi }{6}-isin\frac{107\pi }{6})$$$$=2cos\left(\frac{107\pi }{6}\right)+i\left(0\right)$$$$so{I}_m\left(Z\right)=0$$

Answered by tanmay.chaudhury50@gmail.com last updated on 01/Dec/18

$$1)questionincomplete$$$$$$

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