As an example, the field of real numbers is not algebraically closed, because the polynomial *x*^{2} + 1 has no real zero.
By contrast, the field of complex numbers is algebraically closed, which is the content of the fundamental theorem of algebra.

Every field *F* has an "algebraic closure", which is the smallest algebraically closed field of which *F* is a subfield. Each field's algebraic closure is unique up to isomorphism. In particular, the field of complex numbers is the algebraic closure of the field of real numbers.