Beacuse 
sums up in one little symbol all the nuances and strangeness of math concepts that are so close, but just a little beyond my reach of understanding. And here's why.
, or 
, is equal to the square root of negative 1, multiplied by itself three times.
It's a number that's even weirder than 
itself. Not only is it unrepresentable by any 'real' number as we understand it, it's also the opposite of that strange imaginary unit.
The imaginary unit is a concept I still struggle with. Not because I can't operate with it - quite the opposite; out of everything that I've been taught this semester, working with complex numbers has been (ironically) on the easier end. I mean that I struggle with its very existence. Because it doesn't exist. But, in fact, it does exist. Without it, the world doesn't work. But with it, mathematical logic as I'd understood it for over two decades also doesn't work. As far as I've been able to tell, all mathematics is counting. And here exists a set of numbers, all introduced by , that is by its very nature, uncountable!
, as I inferred above, is equal to 
. And 
. But, hang on. If you were to take the a negative number and square it, you can't possibly end up with a negative number. A negative times a negative is a positive. So, ^2 = |-1| = 1 $)
. But, ^2 = -1 $)
because mathematicians defined it to be so. 
. Deal with it, bucko.
I'm sure that there are many proofs as to why this works, and it's not all just "Take it on faith, Simon, it works," but it's still one of those things I struggle with. Not the use, but the why and how behind it's use. I'm also sure that I'll get over this question in my mind and suddenly, it's existence will make perfect sense. There will be other mathematical concepts, though, that I struggle to fully understand, and get the meaning behind. For many calculus students I'm told it's the delta-epsilon proof. Everyone has their own. And I'll have more than this one. And so is the symbol for every concept of math that people struggle with daily. Because I've defined it to be so!
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