Why is it mathematically consistent to allow imaginary numbers but prohibit division by zero?

Question

Couldn’t the result of division by zero be “defined”, just like the square root of -1?

Edit: Wow, thanks for all the great answers! This thread was really interesting and I learned a lot from you all. While there were many excellent answers, the ones that mentioned Riemann Sphere were exactly what I was looking for:

https://en.wikipedia.org/wiki/Riemann\_sphere

TIL: There are many excellent mathematicians on Reddit!

In: 1691

Answer 1

>Couldn’t the result of division by zero be “defined”

Sure. You can. In a projective real line, x/0 is defined as unsigned infinity if x is not also 0.

But it needs to be emphasized that projective real numbers are not real numbers. And similarly, complex number is not a real number.