Why is something divided through zero not treated similar like an imaginary number?

Question

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

Answer 1

Can this be answered in ELI5 terms? I don’t know enough math to be able to address this, but did stumble over this link to a wikipedia article on wheel theory ( https://en.wikipedia.org/wiki/Wheel_theory ) which says
> Wheels are a type of algebra, in the sense of universal algebra, where division is always defined. In particular, division by zero is meaningful.