I was intrigued by the thread because it was so quirky and so different from everything else, but it's difficult to come up with a plot for it (unless one leaves the initial premise behind).

It's true that imaginary numbers do have applications in the real world. They are used by electrical engineers for instance (I think in connection with capacitance). For some reason, they tend to use "j" as the symbol rather than "i", though.

There are arguably 5 fundamental constants in mathematics: 0, 1, pi, e and i. This beautiful equation, known as Euler's Identity links all five:

e^(i*pi) + 1 = 0 (where ^ means raise to the power).

See:

http://en.wikipedia.org/wiki/Euler%27s_identity
Benjamin Pierce, after proving the formula in a lecture, said, "Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth."

Now from the sublime to the practical: Being a Brit, I'm not familiar with the US school system, so I hope it was realistic to have Mr Jones address our heroine by her first name and for her to call him "Mr Jones". How old would our heroine be, if she's in 12X?