Exercise 2, § 2

Show that, if $f$ is any polynomial with complex coefficients, not identically zero, there exists a real number $r > 0$ such that

whenever $|z| \geq r$. Hence, with the help of Exercise 1 and Weierstrass' theorem (Chapter IV, § 6, no. 1, Theorem 1), give another proof of the fact that $\mathbf{C}$ is algebraically closed (consider the function $f$ on the compact set of points $z$ such that $|z| \leq r$).