Considerations on the probability density in complex space

A probability density is proposed in complex space. This probability density is defined by replacing $x$ with $z$ in the Born probability density of quantum mechanics, and it is real valued and non-negative in complex space. In addition, the Eulerian rate equation for the probability density is derived, and the rate of change of the probability density is determined by the total energy density. Furthermore, this complex-extended Born probability density correctly reflects information of the trajectory dynamics for the wave function in complex space.