Fundamental theorem of algebra via Rouché's theorem

Apply Rouché’s Theorem to prove the Fundamental Theorem of Algebra: If

\[ P _ { n } ( z ) = a _ { 0 } + a _ { 1 } z + \cdots + a _ { n - 1 } z ^ { n - 1 } + a _ { n } z ^ { n } \quad ( a _ { n } \neq 0 ) \]

is a polynomial of degree n, then it has n zeros in \(\mathbb { C } .\)