Sol.\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^6 =
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We want to compute $z^6$. First, we write $z$ in polar form. The numerator is $\sqrt{3}-i = 2(\frac{\sqrt{3}}{2} - \frac{1}{2}i) = 2(\cos(-\frac{\pi}{6}) + i\sin(-\frac{\pi}{6}))$. The denominator is $\sqrt{3}+i = 2(\frac{\sqrt{3}}{2} + \frac{1}{2}i) = Show more…
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