Freeflows
Complex Polynomial Solutions
The solutions to $ z^4 = 4 - 4i \sqrt{3} $ can be expressed in the form \begin{align*} z_1 &= r_1 (\cos \theta_1 + i \sin \theta_1), \\ z_2 &= r_2 (\cos \theta_2 + i \sin \theta_2), \\ z_3 &= r_3 (\cos \theta_3 + i \sin \theta_3), \\ z_4 &= r_4 (\cos \theta_4 + i \sin \theta_4), \end{align*}where $ r_k > 0 $ and $ 0^\circ \le \theta_k < 360^\circ $. Find $ \theta_1 + \theta_2 + \theta_3 + \theta_4, $ in degrees.
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