The value of frac{(cos alpha + i sin alpha)(c | vedclass

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(B) Using the property of complex numbers in polar form,$(\cos 	heta_1 + i \sin 	heta_1)(\cos 	heta_2 + i \sin 	heta_2) = \cos(	heta_1 + 	heta_2

Vedclass · Accepted Answer

$\cos (\alpha + \beta - \gamma - \delta) + i \sin (\alpha + \beta - \gamma - \delta)$

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(B) Using the property of complex numbers in polar form,$(\cos 	heta_1 + i \sin 	heta_1)(\cos 	heta_2 + i \sin 	heta_2) = \cos(	heta_1 + 	heta_2) + i \sin(	heta_1 + 	heta_2)$.Applying this to the numerator: $(\cos \alpha + i \sin \alpha)(\cos \beta + i \sin \beta) = \cos(\alpha + \beta) + i \sin(\alpha + \beta)$.Applying this to the denominator: $(\cos \gamma + i \sin \gamma)(\cos \delta + i \sin \delta) = \cos(\gamma + \delta) + i \sin(\gamma + \delta)$.Now,using the division property $\frac{\cos 	heta_1 + i \sin 	heta_1}{\cos 	heta_2 + i \sin 	heta_2} = \cos(	heta_1 - 	heta_2) + i \sin(	heta_1 - 	heta_2)$:$\frac{\cos(\alpha + \beta) + i \sin(\alpha + \beta)}{\cos(\gamma + \delta) + i \sin(\gamma + \delta)} = \cos((\alpha + \beta) - (\gamma + \delta)) + i \sin((\alpha + \beta) - (\gamma + \delta))$$= \cos(\alpha + \beta - \gamma - \delta) + i \sin(\alpha + \beta - \gamma - \delta)$.

The value of $\frac{(\cos \alpha + i \sin \alpha)(\cos \beta + i \sin \beta)}{(\cos \gamma + i \sin \gamma)(\cos \delta + i \sin \delta)}$ is

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