I'm poorly placed to describe them as a lowly engineer. The idea is to define an additional number which follows the usual rules of algebra but has the additional property that when multiplied by itself you get -1. I believe it was introduced to find the roots of quadratic equations previously considered insoluble, however they have since turned up all over the place. The idea was widely ridiculed as being a "made up" number, which overlooks the issue that all the others are also "made up" numbers in much the same sense. Occasionally the solution to a problem is most cleanly expressed in terms of complex numbers, other times the solution to a problem starts off with real numbers, and ends with a real number, but passes through complex numbers en route.
I'm partway through a book by
Penrose which I would certainly recommend, though much of it is beyond me his love of physics is infectious.
I'm fairly confident that professional physicists would agree with me that it is optimistic to believe that the universe obeys mathematical laws. They are developing a framework which models (or describes) reality with varying success. The idea that the universe itself behaves as we tell it to is fairly insane.
edit: Oh damn it, curiosity is going to lead to reading the linked article
edit2: Linked article was indeed a waste of time. Yes, there are properly referenced formulae in there, and yes they are combined reasonably. There are a lot of required assumptions which are not stated, there is no apparent conclusion, and the author is pleased by two numbers being close to each other when they're two orders of magnitude apart. It is thoroughly ridiculous to conclude based on this brief paper that the universe is mathematical in nature, so I'm back to my original statement.
Your opening post looks to be the scribblings of a retard. Congratulations for trying to further your knowledge of the universe, but perhaps you're starting off too high. Statistical quantum mechanics isn't all that easy to follow.