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Complex Numbershard
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Let zzz be a complex number such that z5=1z^5 = 1z5=1. Consider the polynomial P(w)=∑k=04(w−zk)P(w) = \sum_{k=0}^{4} (w - z^k)P(w)=∑k=04​(w−zk). If P(w)=0P(w) = 0P(w)=0 has a unique solution for www, what is that solution?