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

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 if and only if $\ds \prod_{n \mathop = 1}^\infty \paren {1 + \size {a_n} }$ is convergent.