A Direct Proof and a Transcendental Version
of the Fundamental Theorem of Algebra via
Cauchy’s Theorem
Bao Qin Li
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.
The Fundamental Theorem of Algebra (or FTA) states that every nonconstant polynomial
p.z/ D anzn C an