In general, one thinks of complex numbers as being absolutely required in Quantum Physics but as being optional in Classical Physics. But what about modern classical electromagnetic field theory (gauge theory) in which the electromagnetic field is coupled to the field of charged particles by essentially adding the electromagnetic potential to the (derivative of) complex phase of the field of charged particles (co-variant derivative)? It seems that this is a case in Classical Physics in which complex numbers are required. Comments? Thanks in advance.