[akoboldfrying]

I think it's the same reason why negative numbers were invented: It lets you do more with algebra than you could before (some of which, like raising something to a power leading to a sine wave is pretty weird, but turns out to be useful in engineering, etc.), and everything else still "just works" the same way as before.

(Admittedly the applications of negative numbers are much more obvious.)

[fuzztester]

And why zero was invented.