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If the root is not on the unit circle, say it is $r(\cos\theta+ i\sin\theta)$ where $r\neq 1$, then the sequence is $r^n(\cos(n\theta)+i\sin(n\theta))$. The modulus $r^n$ is either increasing or decreasing, so it cannot repeat.
Hello Dr. Kevin Wang,
Thanks! I got it!
Tina Jin
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