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Question Number 137468 by ZiYangLee last updated on 03/Apr/21

$$\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$(\cos 1°+i\sin 1°)(\cos 2°+i\sin 2°)\dots (\cos 359°+i\sin 359°).$$

Answered by mr W last updated on 03/Apr/21

$$=e^{\frac{1}{180}\pi i}{e}^{\frac{2}{180}\pi i}...e^{\frac{359}{180}\pi i}$$$$=e^{\frac{1+2+...359}{180}\pi i}$$$$=e^{359\pi i}$$$$=e^{\pi i}$$$$=-1$$

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