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

I highly recommend this video series on why imaginary numbers are actually real (and the name imaginary is stupid)