Im stuck on a textbook question that has no previous examples. Express $\displaystyle \left(\frac{\sqrt{3}-i}{2}\right)^{101}$ in cartesian form.

OK. So i know De moivre's Theorem but not sure if i can use it here (and thats going away from Cartesian form too)

But could I say that here the form r(cos x + isin x) can be deduced because $\displaystyle \frac{\sqrt{3}}{2} $ is $\displaystyle cos\frac{\pi}{6}$ and then deduce sin.....

But not sure where to go from here!...