The Fundamental Theorem of Algebra Is:

Every polynomial equation of degree n, n>0, with complex coefficients has
at least one complex root.

This is often stated as

Every polynomial equation of degree n with complex coefficients has n
roots in the complex numbers.

In fact, the two statements are equivalent. The second can be proved by
using the first form to know there is a root, and and then repeatedly dividing
the polynomial by one of its roots until its degree becomes zero.

### Internet references

Wikipedia:
Fundamental theorem of algebra

Mathworld:
Fundamental Theorem of Algebra

### Related pages in this website

Other so-called "fundamental" theorems

The Fundamental Theorem of
Arithmetic says every number has exactly one unique prime
factorization.

The Fundamental Theorem of
Calculus says if f is the derivative of F, then the integral from a to
b of f(x) dx is F(b)-F(a).

The webmaster and author of this Math Help site is
Graeme McRae.