Complex analysis 3: Proofs of the fundamental theorem of algebra based on Cauchy’s theorem
Fundamental theorem of algebra(FTA) Every polynomial of degree \(n\geqslant1\) with complex coeficients has a zero in \(\Bbb C\). 我们尝试使用 Cauchy 积分公式来证明代数基本定理. 其实有几个大同小异的证明, 基本的想法是一致的. 第一个证明属于 Anton R. Schep. Proof. Let \(p(z)=z^n+a_{n-1}z^{n-1}+\dotsb+a_1z+a_0\) be a …
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