The incorporation of imaginary elements into physical theories is one of the most difficult practices for a professional physicist to justify to the layman. Of course, if a particular feature, such as isotopic spin symmetry, renders the model a brilliant success, then the physicist can simply reply, "I put it in because it works!"
Superforce: The Search for a Grand Unified Theory of Nature, Chapter 4 (pp. 66-67), Simon & Schuster. 1984