# Fundamental Theorem of Algebra (With Picard's Little Theorem)

DevFeed: [Fundamental Theorem of Algebra (With Picard's Little Theorem)](<https://devfeed.tech/articles/fundamental-theorem-of-algebra-with-picard-s-little-theorem-40261.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/07/fundamental-theorem-of-algebra-with-picards-little-theorem/>)

Published: 2012-02-07T21:30:12Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [complex-analysis](<https://devfeed.tech/tags/complex-analysis.md>), [fundamental-theorem-of-algebra](<https://devfeed.tech/tags/fundamental-theorem-of-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>)

## AI overview

This post proves the Fundamental Theorem of Algebra using Picard's Little Theorem. Assuming basic complex analysis, it argues that a nonconstant polynomial cannot omit both zero and a suitable reciprocal value, because continuity and boundedness would force a zero.

## Source excerpt

This post assumes familiarity with some basic concepts in complex analysis, including continuity and entire (everywhere complex-differentiable) functions. This is likely the simplest proof of the theorem (at least, among those that this author has seen), although it stands on the shoulders of a highly nontrivial theorem. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way.