Application of Complex Numbers
If you consider Real Power and Imaginary Power  we are talking about resistive power and reactive power with energy stored in inductors, and capacitors.  The vector sum of both is called "apparent power"

Even in mechanical systems there are complex reciprocal devices with stored energy in flywheels or springs.  Inductors and Capacitors are similar in that they can store energy , in math called imaginary value. 

But when an inductor opens current and arcs, it turns in to real energy similar to shorting out a capacitor into some resistance.  Although this is a crude example like putting a crowbar brake across a flywheel.