Definition:Absolute Convergence of Product/Complex Numbers

Definition
Let $(a_n)$ be a sequence in $\C$.

Then the infinite product $\displaystyle\prod_{n=1}^\infty(1+a_n)$ is absolutely convergent iff $\displaystyle\prod_{n=1}^\infty(1+|a_n|)$ is convergent.

Also see

 * Absolute Convergence of Infinite Product of Complex Numbers