and a quantum computer could have a number be simultaneously 1 and -1 due to superposition would that allow the square root to be solved by a quantum representation that is a combination of both?
A regular computer can already represent i. You can do complex math on them fine, it's just a matter of specifying what the bits mean and the rules they follow.
I don't think that has anything to do with quantum or not, and I'm not sure what there is to "solve" about the sqrt(-1). We know what it is, it's just called i in the complex numbers (by definition). There's not another level to go down and explore. (in some other number systems, like the reals, sqrt(-1) just doesn't exist because no number times itself is -1).
I don't think that has anything to do with quantum or not, and I'm not sure what there is to "solve" about the sqrt(-1). We know what it is, it's just called i in the complex numbers (by definition). There's not another level to go down and explore. (in some other number systems, like the reals, sqrt(-1) just doesn't exist because no number times itself is -1).