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Question Number 176366 by doline last updated on 17/Sep/22

$$donnerlaformetrigonometriquede(1-i\sqrt{}3)(1+i)(cos\theta -isin\theta )$$

Answered by Ar Brandon last updated on 17/Sep/22

$$\left(2e^{-\frac{\pi }{3}i}\right)\left(\sqrt{2}{e}^{\frac{\pi }{4}i}\right)\left(e^{-i\theta }\right)=2\sqrt{2}{e}^{(-\frac{\pi }{3}+\frac{\pi }{4}-\theta )i}$$$$=2\sqrt{2}{e}^{-(\frac{\pi }{12}+\theta )i}=2\sqrt{2}(\cos (\theta +\frac{\pi }{12})-i\sin (\theta +\frac{\pi }{12}))$$

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