Analytical support for recent numerical work in process simulation in the complex domain is discussed. In particular, the observation that nondegenerate singular points are saddle points of the two-norm on the complex domain is proved rigorously and its numerical implications are discussed. The isothermal isobaric flash problem admits only real-valued two-phase solutions, provided that the feed conditions are real. Both single- and multivariable chemical process examples illustrate the theoretical results.