One way to prove this statement is to examine the Sylow 2-subgroups of the Galois group of the Gauss plane.
One way to prove this statement is to examine the Sylow 2-subgroups of the Galois group of the Gauss plane. The minimum modulus principle applied to a closed disk around the origin gives a complex analytic proof of this theorem. A topological proof can be obtained by using the invariance of the winding number under continuous deformations. This theorem implies that the complex numbers are the algebraic closure of the reals and also holds for polynomials with complex coefficients. For 10 points, name this theorem that states that an nth-degree polynomial with complex coefficients has exactly n roots.
One way to prove this statement is to examine the Sylow 2-subgroups of the Galois group of the Gauss plane.
{f}undamental {t}heorem of {a}lgebra