Simple applications of complex numbers I've been helping a high school student with his complex number homework (algebra, de Moivre's formula, etc.), and we came across the question of the "usefulness"  of "imaginary" numbers - If there not real, what are they good for?
Now, the answer is quite obvious to any math/physics/engineering major, but I'm looking for a simple application that doesn't involve to much. The only example I've found so far is the formula for cubic roots applied to $x^3-x=0$, which leads to the real solutions by using $i$.
Ideally I'd like an even simpler example I can use as motivation.
Any ideas?

Point is that "imaginary" represents sine waveform that is quite real. So if you need so add or to subtract two trigonometric signals, you will do it more easily with complex numbers (phasor) approach, rather then directly. See more:
http://www.cirvirlab.com/index.php/electric/98-phasor-ac-signal-addition-and-subtraction.html 
