Exercise 3, § 3

Let $(z_i)_{i \in I}$ be a family of complex numbers such that $\prod_{i \in I} |z_i| = +\infty$, (resp. $\prod_{i \in I} |z_i| = 0$). Show that the family $(z_i)$ is multipliable in the space $\tilde{\mathbf{C}}$ (§ 4, no. 3) and that its product is $\infty$ (resp. 0).