<Snipped quote by whizzball1>
No, it's called imaginary because no number can be squared to return a negative number; you would be forced to invent an entirely new number system- which someone did. I hold that equations could likely be solved with another formula, using strictly real numbers. Regarding faster than light, there is no reason a particle moving at that speed would somehow change formulas to include imaginary principles, and while there may not be mathematical objections (technically), there are physics objections, due to anything traveling at the speed of light would require infinite energy, or no mass. Because, in this aspect (due to formulas and concept) mathematics and physics are intertwined, there is no way of separating them, causing a concept violating physics to violate mathematical laws, and vice versa.
The entirely new number system exists just as the irrational numbers were entirely new, but they exist as well. We invented the irrationals to square the circle. We invented the complex numbers to take the square root of negative numbers. The real numbers are either positive, negative, or zero. Any negative number multiplied by itself is positive, just as any positive number, and 0 squared is 0. No real number can be squared to arrive at a negative number. Thus, we came up with the complex numbers. But people didn't like that, and they called it imaginary. The imaginary numbers are no more imaginary than the irrational numbers are irrational--that is, not at all.
Audacious