Displaying Complex Functions

In Wave Mechanics, the state of a system of particles is represented by a wave function. The first problem with visualizing wave functions is that they are complex-valued. A wave function assigns a number to every point in the underlying coordinate space, and that number is a complex number. Authors often try to deal with this by showing separate plots of the real and imaginary parts of the wave function. This approach, while factually correct, can hide the essential continuity of many wave functions. As an example, here are plots of the real and imaginary parts of a simple complex exponential, $\Phi = exp^{-\imath kx}$;

The top curve is the real part, the bottom the imaginary part.