<s>[INST] complex number with high powers The question:
$\frac{(-1-\sqrt{3}i)^{73}}{2^{73}}$
I really do not even know where to begin. Am I suppose to expand $(-1-\sqrt{3}i)$ 73 times? 
 [/INST] Ok, what I got was:
$(-\frac{1}{2}-\frac{\sqrt{3}}{2}i)^{73}$
$|z| = \sqrt{(-1/2)^2+\sqrt{3}/2} = \sqrt{1} = 1$ 
tan$^{-1}$ ($-.5/ \sqrt{3}/2) = \frac{-2}{3}2\pi$
$z^{73} = 1($cos$(\frac{-2}{3}2\pi)+i$sin$(\frac{-2}{3}2\pi)$) 
$z = 1^{73}($cos$(\frac{-2}{3}2\pi*73)+i$sin$(\frac{-2}{3}2\pi8*73)$) 
= $-.5 + \frac{\sqrt{3}}{2}$ which is the same answer had I not multiplied by 73
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