The Fundamental Theorem of Algebra

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

Let h(z) = zn + an-1*zn-1 + ...+ a 1*z + a0 be a complex polynomial of degree n > 0. Let f(z) = zn and g(z) = an-1*zn-1 + ... + a1*z + a0. |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) = zn in the disc of radius R centered around the origin.