The value of - 1 + i 3 1 - i 30 is :

${\left(\frac{-1+\sqrt{3}i}{1-i}\right)}^{30}={\left(\frac{2\cos \left(\frac{2\pi }{3}\right)+i\sin \left(\frac{2\pi }{3}\right)}{\sqrt{2}\left(\cos \frac{\pi }{4}-i\sin \frac{\pi }{4}\right)}\right)}^{30}$

$=\frac{2^{30}(\cos 20\pi +i\sin 20\pi )}{2^{15}\left(\cos \frac{15\pi }{2}-i\sin \frac{15\pi }{2}\right)}$

$=\frac{2^{15}(1+0i)}{(0+i)}=-2^{15}i$