Question:
The value of $\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}$ is
Correct Option: , 3
Solution:
$\because-1+\sqrt{3} i=2 \cdot e^{\frac{2 \pi}{3} i}$ and $1-i=\sqrt{2} \cdot e^{-\frac{i \pi}{4}}$
$\therefore\left(\frac{-1+\sqrt{3} i}{1-i}\right)^{30}=\left(\sqrt{2} e^{\left(\frac{2 \pi}{3}+\frac{\pi}{4}\right)}\right)^{30}$
$=2^{15} \cdot e^{-\frac{\pi}{2} i}=-2^{15} \cdot i$
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