Word Count : 333

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We are given the following: * $S^1 = \{ z \in \mathbb{C}^* \mid |z| = 1 \}$, the unit circle in the complex plane — i.e., the set of all complex numbers with modulus 1. * $U_n = \{ z \in \mathbb{C}^* \mid z^n = 1 \}$, the group of complex $n^\text{th}$ roots of unity. ________ ___ _______ _______ ____ _____.
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