This post is in General Math because it is focuses on the complex plane and justifications for using it. I do not understand what it means for a wave to have an imaginary part. I can understand expressing a wave as e^(iθ) and then extracting the information you want since complex exponentials are easier to work with than adding sines and cosines with different arguments. But according to the http://en.wikipedia.org/wiki/Schrödinger_equation#Derivation", we do not use this form for convenience but because the wave really has imaginary components. What does this mean, that the wave has imaginary components?