Definition:Absolute Convergence of Product/Complex Numbers

Definition
Let $\left\langle{a_n}\right\rangle$ be a sequence in $\C$.

Then the infinite product $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + a_n}\right)$ is absolutely convergent $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + \left\vert{a_n}\right\vert}\right)$ is convergent.

Also see

 * Absolute Convergence of Infinite Product of Complex Numbers for equivalent characterizations