We extend the notion of complex B-splines to a multivariate setting by employing the relationship between
ordinary B-splines and multivariate B-splines by means of ridge functions. In order to obtain properties of
complex B-splines in Rs, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional
simplices. Based on this generalization several identities of multivariate complex B-splines are exhibited.