# 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 , $\mathbb{C}$ is algebraically closed.

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

Title fundamental theorem of algebra FundamentalTheoremOfAlgebra 2013-03-22 12:18:56 2013-03-22 12:18:56 Mathprof (13753) Mathprof (13753) 14 Mathprof (13753) Theorem msc 12D99 msc 30A99 ComplexNumber Complex TopicEntryOnComplexAnalysis ZeroesOfDerivativeOfComplexPolynomial