摘要：伴随漫长的解方程历史探索中，数学家得出一元多次方程解与次数关系的代数学基本定理，一直以来，学者们给出了不同的方法来证明这个定理。代数学基本定理在代数学中占有非常重要的地位，这篇论文将叙述代数学基本定理的内容，并用复变函数理论中的刘维尔定理、儒歇定理、辐角原理、最大模原理、最小模原理、留数定理、柯西定理来证明代数学基本定理，并对这些证明方法进行说明、比较与总结。

关键词：代数学基本定理； 辐角原理； 最大模原理； 最小模原理

Abstract:With a long history of exploration in the solution of equations, mathematicians come to a dollar many times the relationship between the number of equations and the fundamental theorem of algebra, has been, have given different ways to prove the theorem. Fundamental theorem of algebra in the algebra plays a very important position, this paper will describe the contents of the fundamental theorem of algebra and complex function theory with the Liouville theorem, Confucianism break theorem, argument principle, maximum modulus principle, the minimum Modulus principle, residue theorem, Cauchy's Theorem to prove the fundamental theorem of algebra, and the proof are described, compared and summarized.

Keywords：Fundamental theorem of algebra; Argument principle; maximum modulus principle; minimum modulus principle