The amplitude of frac{1 + sqrt{3}i}{sqrt{3} + | vedclass

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Question

(A) Let $z = \frac{1 + \sqrt{3}i}{\sqrt{3} + i}$.Using the property of arguments,$	ext{amp}\left(\frac{z_1}{z_2}ight) = 	ext{amp}(z_1) - 	ext{amp

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$\frac{\pi}{6}$

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(A) Let $z = \frac{1 + \sqrt{3}i}{\sqrt{3} + i}$.Using the property of arguments,$	ext{amp}\left(\frac{z_1}{z_2}ight) = 	ext{amp}(z_1) - 	ext{amp}(z_2)$.$	ext{amp}(1 + \sqrt{3}i) = 	an^{-1}\left(\frac{\sqrt{3}}{1}ight) = \frac{\pi}{3}$.$	ext{amp}(\sqrt{3} + i) = 	an^{-1}\left(\frac{1}{\sqrt{3}}ight) = \frac{\pi}{6}$.Therefore,$	ext{amp}(z) = \frac{\pi}{3} - \frac{\pi}{6} = \frac{\pi}{6}$.

The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} + i}$ is

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