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Question Number 121705 by bemath last updated on 11/Nov/20

Answered by MJS_new last updated on 11/Nov/20

$$\mathrm{cis}x=\cos x+\mathrm{i}\sin x={\mathrm{e}}^{\mathrm{i}x}$$$$16°=\frac{4\pi }{45};44°=\frac{11\pi }{45};62°=\frac{31\pi }{90}$$$$\frac{{12\mathrm{e}}^{\frac{4\pi }{45}\mathrm{i}}}{{3\mathrm{e}}^{\frac{11\pi }{45}\mathrm{i}}{2\mathrm{e}}^{\frac{31\pi }{90}\mathrm{i}}}={2\mathrm{e}}^{\mathrm{i}\pi (\frac{4}{45}-\frac{11}{45}-\frac{31}{90})}={2\mathrm{e}}^{-\mathrm{i}\frac{\pi }{2}}=-2\mathrm{i}$$

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