## The Fundamental Theorem of Algebra

### Every complex polynomial of degree n > 0 has exactly n roots in the complex plane.

### Let h(z) = z^{n} + a_{n-1}*z^{n-1} + ...+ a _{1}*z + a_{0} be a complex polynomial of degree n > 0. Let f(z) = z^{n} and g(z) = a_{n-1}*z^{n-1} + ... + a_{1}*z + a_{0}. |f(z)| > |g(z)| for |z| = R where R is sufficiently large, so h(z) = f(z) + g(z) has the same number of roots as f(z) = z^{n} in the disc of radius R centered around the origin.