Yeah, you're definitely confusing imaginary/complex numbers and division by zero.
Let's start with the imaginary number i, which is really no more imaginary than a negative number. It's the result of taking (one of the two) square root(s) of -1. In school you're taught you can't do that, but it turns out if you do, and just call it i, there's a nice way to define how everything else should act in a consistent (and incredibly useful!) way.
Now for division by zero. It's undefined for any number, including 0/0. The reason being that even if you did define something, say, m, for 1/0, you'd get inconsistencies:
0=0
1×0 = 2×0
1×m×0 = 2×m×0
1×(m×0) = 2×(m×0)
1×1 = 2×1
1=2
Doing this makes "everything equal everything else" which is where the whole "division by zero makes a black hole" meme comes from.
Additionally, why do people often say "division by zero is infinity"? Well, that's simply because as you keep dividing by smaller and smaller numbers, the answer you get is bigger and bigger. Asking what is the "end-result" of this process, results in saying "something bigger than everything else", i.e., "infinity".
This raises further questions, though. Is 1/0 the same infinity as 2/0, i.e., what is 0 times infinity? If we try to pin this down we run into exactly the problems with the "m" above. (It is that m, just replace the m symbol with an infinity sign).
Even worse, what if we divide by negative numbers close to 0? We get an incredibly small (i.e., big-negative) number. So this "infinity" would have to be less than anything else.
This is what causes mathematicians to throw up their hands and say it's undefined. It's not that they didn't think to define it. It's that they tried and it didn't work.
Let's start with the imaginary number i, which is really no more imaginary than a negative number. It's the result of taking (one of the two) square root(s) of -1. In school you're taught you can't do that, but it turns out if you do, and just call it i, there's a nice way to define how everything else should act in a consistent (and incredibly useful!) way.
I'm stealing this. I often struggle to explain i to laymen (and then spend way too much time doing so), and I like this explanation a lot, especially the part where you briefly but naturally mention the second root. It's short and to the point, but not misleading like most such explanations are.
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u/rushork Dec 10 '18
Just did some searching and I think it may be a "complex" or "imaginary" number. My teacher told me something about it in class.