fundamental theorem of algebraFundamentalTheoremOfAlgebra2002-02-13 09:09:012006-12-03 09:00:25Theorem% this is the default PlanetMath preamble. as your knowledge
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\begin{thm}
Let $f \in \mathbb{C}[z]$ be a non-constant polynomial. Then there is a$z\in\mathbb{C}$ with $f(z)=0$.
\end{thm}
In other \PMlinkescapetext{words}, $\mathbb{C}$ is algebraically closed.
As a corollary, a non-constant polynomial in $\mathbb{C}[z]$ factors completely
into linear factors.