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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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