One proof of this theorem uses Liouville's theorem, that any bounded function differentiable on the complex plane is constant.
One proof of this theorem uses Liouville's theorem, that any bounded function differentiable on the complex plane is constant. An attempt to prove this theorem by d'Alembert was incomplete, and it was eventually proven by Gauss. It implies that every algebraic extension of the real numbers is isomorphic to the field of either real or complex numbers. In 1806 Argand stated this theorem for complex coefficients. A corollary of this theorem is that the field of complex numbers is closed. For 10 points, name this theorem that states that a polynomial of degree n has n roots in the complex plane. 
One proof of this theorem uses Liouville's theorem, that any bounded function differentiable on the complex plane is constant.
fundamental theorem of algebra 