# Fundamental Theorum of Algebra an i.

1. Jun 29, 2009

### Starwatcher16

Does the Fundamental Theorum of Algebra prove that imaginery numbers have to exist for our number system to be complete?

2. Jun 29, 2009

### g_edgar

Something other than real numbers have to exist for the equation $$x^2+1=0$$ to be solvable. But I wouldn't say it the way you did.

3. Jun 29, 2009

No. The Fundamental Theorem of Algebra implicitly assumes the existence of complex numbers: it states that every polynomial of degree $$n$$ with complex coefficients has at least one zero. (You sometimes see this written to say that if you count the zeros' multiplicities then the number of zeros equals the degree of the polynomial).