Recently, Akiyama et al. introduced so-called shift radix systems. These simple dynamical systems form a common generalization of several well-known notions of number systems like beta numeration and canonical number systems. In the present paper we generalize shift radix systems as follows: for (r1, . . . , r d ) ∈ C d we study mappings where for x ∈ C we set ⌊x⌋ = ⌊ℜx⌋ + i⌊ℑx⌋. We study basic dynamical properties of this class of mappings and relate them to known notions of number systems.