# The Fundamental Theorem of Algebra The fundamental theorem of algebra postulates that **any polynomial** with complex coefficients **of degree $n$ has exactly $n$ complex roots, when accounting for multiplicity**[^1] i.e. root with multiplicity $k$ is counted $k$ times. [^1]: [[Polynomials#Root Multiplicity]] No simple proofs exist, simplest proofs use complex analysis. ## Resources - [Fundamental Theorem of Algebra](https://brilliant.org/wiki/fundamental-theorem-of-algebra/). Brilliant.org.