So in grade 7 math we learned that you can’t take the square root of negative numbers because any number squared is always going to be positive. A few years later we learn that you can actually calculate with the square root of negative numbers. You replace the square root from -1 with i. So why aren’t we replacing something divided by zero also with a letter?
In: Mathematics
> You replace the square root from -1 with i.
There is quite a bit more to it than just making up a new symbol for √-1 and calling it i.
Imaginary (and complex) numbers are a two-dimensional extension of the one-dimensional number line, and i = √-1 is a natural consequence of that. In two dimensions, you can think of multiplying by -1 as a 180^(o) rotation. Multiplying by i is a 90^(o) rotation, so doing it twice is the same as 180^(o). That means i x i = -1, and √-1 = i.
There is no similar extension, at least none that I am aware of, that cleanly replaces 1 / 0 with some discrete value.
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