Frome the introduction: The purpose of this paper is to show an algorithm to produce the complex \(\lambda\)-expansion of \(z\in \mathbb C\), \(z=\sum_{n=k_0}^\infty a_n\lambda^{-n}\), \(a_n\in \Gamma\), where \(\gamma\) is a finite digit set of \(\mathbb Z[\lambda]\). For this purpose, we introduce a complex Pisot number \(\lambda\).