I'm having problems to solve these kind of tasks with powers - like:

$\displaystyle \left ( \frac{\sqrt{3}-i}{1+i} \right )^{24}$

Or

$\displaystyle \frac{(\sqrt{3}-i)^{13}}{(1+i)^{16}} + \frac{(\sqrt{3}+i)^{13}}{(1-i)^{16}}$

I try with racitonalizing but i don't get much. Would appreciate any kind of help.

Thanks,

Flamuri