I know how to find the roots of this answer, but I believe this question is asking for something different as I don't believe I am expected to write out all 22 roots. I am not looking for the answer exactly, but I would like some help getting started on the right track as I don't know how to begin the problem. Thanks.
2026-03-29 05:34:55.1774762495
Find the real and imaginary parts of $z^{22}=\sqrt{3} - i$
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Hint: $$\sqrt{3}-i = 2e^{-\frac\pi 6 i}$$
This is true by Euler's formula.