The application of this formalism in a purely electronic framework, sometimes referred to as exact electron factorization, to distinguish it from its electro-nuclear counterpart, sits well within the scope of density-functional theory (DFT), both in its pure Hohenberg-Kohn version and in its more popular Kohn-Sham (KS) one . In this context, the exact factorization has been adopted to gain physical insight in the effective potentials that map the many-body (electronic) problem into a one-body problem . There are stark features of the Kohn-Sham potential as well as of the effective potential in orbital-free DFT , in the form of peaks and steps, that are extremely hard to model but have been shown to be paramount for the proper description of phenomena such as molecular dissociation or Mott-Hubbard transitions . Such features have been extensively studied in simple systems for which accurate or exact solutions can be calculated. They have been attributed to specific terms of the total potential, named the kinetic potential, v kin , and the N -1 potential, v N -1 , * that were identified using the exact factorization and are responsible for the peaks and the step(s) features, respectively . However, these local potentials have been defined and studied only for real wavefunctions. This restriction can be imposed with no loss of generality for ground states but it is limiting in the study of excited states where complex wavefunctions may occur. For complex wavefunctions, extra terms, in addition to the well-studied local potentials, are expected to appear, notably a vector potential .