Comment by direwolf20

The whole idea of an imaginary number is that it squares to a negative number. Everything else is accidental. Nobody expected that exp(i*a)=cos(a)+i*sin(a). Totally wacky discovery.

Imaginary numbers don't work in 3D, by the way. The most natural representation of a 3D rotation is a normalized 4D quaternion, and it's still pretty weird.