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Roots of P' are in {z: |P(z)| = 1}

Source: Miklós Schweitzer 2019, Problem 7

December 27, 2019
algebracollege contestsMiklos Schweitzercomplex analysis

Problem Statement

Given a polynomial PP, assume that L={z∈C:∣P(z)∣=1}L = \{z \in \mathbb{C}: |P(z)| = 1\} is a Jordan curve. Show that the zeros of P′P' are in the interior of LL.
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