How to prove that an equation of degree n of one variable must have complex roots

How to prove that an equation of degree n of one variable must have complex roots

This is a simple conclusion of functions of complex variables. We can use Liouville's theorem: a bounded entire function must be a constant. If a polynomial of degree n (a polynomial is an entire function) has no root, then its reciprocal is analytic in the extended complex plane (the point at infinity is a removable singular point), If its reciprocal is constant (because its reciprocal is bounded), then it is constant itself. This is in contradiction with the fact that it is a polynomial
In addition, it will be very difficult to prove by algebraic method