It is a strict requirement that physical observables should be real-valued; the position and momentum of a particle obeying the Newtonian equations of motion are both real, and any dynamical variables derived from them are also real. The wavefunction in quantum mechanics may be complex-valued, but observables obtained averaged over the square modulus of the wavefunction turn out to be real. Occasionally, one examines the nature of singularities in the complex plane in order to judge whether the system under consideration is completely integrable or not, but in almost all cases complex variables appear only implicitly in the description of physical phenomena. Indeed, there is no serious demand or even motivation to investigate dynamics whose variables are complex.