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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

8:13 pm

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

## 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