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# fundamental theorem of algebra

###### Theorem.

Let $f\in\mathbb{C}[Z]$ be a non-constant polynomial. Then there is a $z\in\mathbb{C}$ with $f(z)=0$.

In other words, $\mathbb{C}$ is algebraically closed.

As a corollary, a non-constant polynomial in $\mathbb{C}[Z]$ factors completely into linear factors.

Related:

ComplexNumber, Complex, TopicEntryOnComplexAnalysis, ZeroesOfDerivativeOfComplexPolynomial

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

12D99*no label found*30A99

*no label found*

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## Recent Activity

Jul 5

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

## Attached Articles

proof of the fundamental theorem of algebra (Liouville's theorem) by Evandar

proof of fundamental theorem of algebra by scanez

fundamental theorem of algebra result by rspuzio

proof of fundamental theorem of algebra (due to d'Alembert) by rspuzio

proof of fundamental theorem of algebra (argument principle) by rspuzio

proof of fundamental theorem of algebra (Rouch\'e's theorem) by Wkbj79

polynomial equation of odd degree by pahio

proof of fundamental theorem of algebra (due to Cauchy) by pahio

proof of fundamental theorem of algebra by scanez

fundamental theorem of algebra result by rspuzio

proof of fundamental theorem of algebra (due to d'Alembert) by rspuzio

proof of fundamental theorem of algebra (argument principle) by rspuzio

proof of fundamental theorem of algebra (Rouch\'e's theorem) by Wkbj79

polynomial equation of odd degree by pahio

proof of fundamental theorem of algebra (due to Cauchy) by pahio