  Many proofs of the fundamental theorem of algebra rely on the fact that the
minimum of the modulus of a complex polynomial over the complex plane is
attained at some complex number. The proof then follows by arguing the minimum
value is zero. This can be done by proving that at any complex number that is
not a zero of the polynomial we can exhibit a direction of descent for the
modulus. In this note we present a very short and simple proof of the existence
of such descent direction. In particular, our descent direction gives rise to
Newton's method for solving a polynomial equation via modulus minimization and
also makes the iterates definable at any critical point.
