Comment by throwaway_2494

> "hey, why do mathematicians keep changing rules on the fly, they just told me square of minus one doesn't exist

Mathematicians aren’t chasing numerical solutions, they’re chasing structure. ℂ isn’t just about solving cubics, it’s about eliminating holes in algebra so the theory behaves uniformly and is easier to build upon.

And as for "changing rules" they haven't changed, they have broadened the field (literally) over which the old rules applied in a clever way to remove a restriction.