Complex polynomial theorem proof?

Please prove that every complex polynomial function f(x) of degree n > or = 1 has at least one complex zero.

p.s Kudos to the cat that knows this without internet help.

Suppose all zeros are real...

f(x) = sum_{i=1}^n (x-z_i), where z_i is in R

then all coefficients are real

Originally posted by fiftyonehz
Suppose all zeros are real...

f(x) = sum_{i=1}^n (x-z_i), where z_i is in R

then all coefficients are real

Originally posted by mtthw
I don't think that's what he's getting at - real numbers are complex.

Yes, geepamoogle said what I meant when I meant what I said.