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The value of $\left(\frac{-1+i\sqrt{3}}{1-i}\right)^{30}$ is:
(1) $-2^{15}$
(2) $2^{15}i$
(3) $-2^{15}i$
(4) $6^5$
$\frac{-1+i\sqrt{3}}{1-i} = \frac{2e^{i2\pi/3}}{\sqrt{2}e^{-i\pi/4}} = \sqrt{2}e^{i11\pi/12}$. Raised to 30th power: $(\sqrt{2})^{30}e^{i \cdot 30 \cdot 11\pi/12} = 2^{15}e^{i55\pi/2} = 2^{15}e^{i3\pi/2} = -2^{15}i$.
BETA
