Well, augmenting reality with an extra dimension containing the thing that previously didn’t exist is the same as “trying and seeing what would happen.” It worked swimmingly for the complex numbers.

No it isn't. The difference between and the values returned by $M a v e r i c k ()$ is that $i$ can be used to prove further theorems and model phenomena, such as alternating current, that would be difficult, if not impossible to model with just the real numbers. Whereas positing the existence of $M a v e r i c k ()$ is just like positing the existence of a finite value $h$ that satisfies $h = \frac{1}{0}$ . We can posit values that satisfy all kinds of impossibilities, but if we cannot prove additional facts about the world with those values, they're useless.