Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?

Question

Why can’t you invent an imaginary number for division by zero like you can for a square root of a negative?

In: Mathematics

Answer 1

You can. In fact there are multiple, conflicting ways to do it. It is sometimes convenient to extend the real line by compactification in such way that infinity = -infinity, like an infinite ‘circle’. Sometimes it is convenient to keep these separate. So we don’t take any of them as *default*, and in the reals themselves we leave 1/0 as undefined.