Complex Numbers Problem Solving 1

Algebra Level 2

If \[x=\cos \frac{\pi}{3}+i\sin \frac{\pi}{3}, y=\cos \frac{5}{3}\pi+i\sin \frac{5}{3}\pi,\] what is the value of \[\left(\frac{x^2}{y}+\frac{y^2}{x}\right)^{6}?\]

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