fundamental theorem of algebra

Theorem.

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

In other , $ℂ$ is algebraically closed.

As a corollary, a non-constant polynomial in $ℂ[Z]$ factors completelyinto linear factors.