Need help proving that: $(1+\cos\alpha+i\sin\alpha)^{n}= 2^{n}\cos^{n}\frac{\alpha}{2}\left(\cos\frac{n\alpha}{2}+i\sin\frac{n\alpha}{2}\right)$
Prove identity involving powers and trigonometric functions
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complex-numbers
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0Hint: $\mathrm e^{\mathrm i\phi}=\cos\phi + \mathrm i\sin\phi$ – 2012-09-30
1 Answers
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Hint: $ 1 + \cos\alpha = 2\cos^2\frac{\alpha}{2} \\ \sin\alpha = 2\sin\frac{\alpha}{2}\cos\frac{\alpha}{2} $
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0@Mykolas You're welcome! – 2012-09-30