Signed two-mode networks have so far predominantly been analysed using blockmodeling techniques. In this work, we put forward the idea of projecting such networks onto its modes. Two projection methods are introduced which allow the application of known dichotomization tool for weighted networks to obtain a simple signed network. It turns out, however, that resulting networks may contain ambivalent ties, defined as conjunctions of positive and negative ties. We show that this requires the reformulation of matrices related to the network and introduce the complex adjacency and Laplacian matrix. These matrices are used to prove some properties related to balance theory including ambivalence.