Is it possible to have a complex number in an objective function and constraints of MIP?

I don't have a background on operations research or optimization algorithms. I am working on balancing the phase of a distribution feeder by optimizing the phase setting of loads connected to it. One method to accomplish this is through mixed-integer programming. I will use electric current to model the system. Now, since electric current is a complex number, I want to know if it's valid to have a complex number on the objective function and constraints of MIP. The phase setting, on the other hand, is the integer one and it's values are either 0 or 1.

[Matt J]

If the objective function is not real-valued, how would you define a "minimum" value for the solver to search for? How would you order objective function values relative to each other so as to define an optimum?