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A Direct Proof and a Transcendental Version of the Fundamental Theorem of Algebra via Cauchy’s Theorem

Bao Qin Li
The American Mathematical Monthly
Vol. 121, No. 1 (January 2014), pp. 75-77
DOI: 10.4169/amer.math.monthly.121.01.075
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.01.075
Page Count: 3
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A Direct Proof and a Transcendental Version of the Fundamental Theorem of Algebra via Cauchy’s Theorem
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Abstract

Abstract We will show that Cauchy’s theorem implies the Fundamental Theorem of Algebra in a direct and elementary manner. Furthermore, the argument can be used to give a transcendental version of the theorem for holomorphic functions or transcendental entire functions.

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