\noindent We study the concept of complementarity, introduced by Bagchi and Quesne in [Phys. Lett. A {\bf 301}, 173 (2002)], between pseudo-Hermiticity weak a rigorous mathematical viewpoint coordinate transformations when system has position-dependent mass. first determine, under modified-momentum, generating functions identifying complexified potentials $V_\pm(x)$ both concepts $\widetilde\et...