Well, first I have to agree with Negative that anything divided by zero is undefined. As such you should simply take the limit as the value in the denominator approaches zero, and use l'Hopital's rule if necessary.

The convention suggested is an interesting idea but I'm not sure how good an idea it is to simply create conventions so late in the mathematical game. The use of i to represent the square root of negative one is really no different that using pi to represent the relationship between the diameter and circumference of a circle. The fact that numbers containing i have sometimes been called "imaginary" is just unfortunate nomenclature as they are just as real and important as the number set with which most people are comfortable.

I myself was not a fan of the complex plane until recently. However, once you realize that all numbers are complex (some just have a zero-size imaginary component) higher-level math makes a lot more sense, and though it may make your life more complicated, you'll have a much better understanding of physical and electical systems.