Imagine, if you will, if division by zero want not undefined. Go ahead, construct as many fact families involving zero as you want. Fun, yes, now you can make whatever number you want, 5/0=200 and 5/0=0.0004, sure, it's all equally valid and you have not contradicted anything, the results are sensible and follow from obvious rules yet they are not useful at all.
Dare I ask, what is your problem with imaginary and complex numbers? It's the name, isn't it? You think that because it has the name imaginary that the numbers do not exist? One could levy the same complaint against zero, or negative numbers, or any number - they don't exist, you're just making shit up. Indeed. There are many systems in nature where two different measurable things can be squared and added to produce a third measurable thing, with electric power as the star example, imaginary numbers are simply a neccesary construction when working on such systems. The other frequently cited example is communications, that is the use of electronics to efficiently encode, send, decode message, say over radio. If you still have any doubts about the usefulness of imaginary numbers and their great many uses, I suggest you consider the following:
https://en.wikipedia.org/wiki/Euler%27s_formulaAs you can see, e, i, pi, and the trigonmetric functions are related. I shouldn't have to explain why, and it would be difficult for me to imagine a logical system where this was not the case.
