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Consider the complex numbers $z_1, z_2, z_3$ and $z_4$ in the following picture,

with the various angles between the line segments marked:  Here, we have that $|z_1| = |z_3| = 3$ and $|z_2| = |z_4| = 2$. Then calculate the ordered list \[ z_1^6, z_2^6, z_3^6, z_4^6.\]Enter in your answers in order, in rectangular form.

 Jan 19, 2019
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 Jan 20, 2019

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