Almira and Romero showed that this statement's falsehood would require that the sphere be  at.
One proof of this statement used the Durand-Kerner method and the ho- motopy continuation principle to achieve a constructive proof, and Rouché's theorem can be used to obtain a short proof. Almira and Romero showed that this statement's falsehood would require that the sphere be  at. The maximum modulus principle is central to a complex-analytic proof of this statement, which implies that every polynomial with complex coe cients can be   factored down to monomials with complex coe cients. This theorem states that the  eld of complex numbers is algebraically closed. For ten points, identify this theorem stating that any complex-valued polynomial has at least one complex root.
One proof of this statement used the Durand-Kerner method and the ho- motopy continuation principle to achieve a constructive proof, and Rouché's theorem can be used to obtain a short proof.
fundamental theorem of algebra [prompt on fundamental theorem, do not accept or prompt on  fundamental theorem of [anything else] , including  fundamental theorem of linear algebra ]