Definition:Absolute Convergence of Product/Complex Numbers/Definition 1

Definition
Let $\sequence {a_n}$ be a sequence in $\C$.

The infinite product $\ds \prod_{n \mathop = 1}^\infty \paren {1 + a_n}$ is absolutely convergent $\ds \prod_{n \mathop = 1}^\infty \paren {1 + \size {a_n} }$ is convergent.

Also see

 * Equivalence of Definitions of Absolute Convergence of Product of Complex Numbers