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

I thought any number divided by zero equaled infinity? Wouldn’t it just be an extra infinity in the formula?