In response to the imaginary number comment ...
Imaginary numbers are a HORRIBLE term.
There is nothing imaginary about the square root of -1. It exists. And is necessary element in what is known as an algebraically closed field.
That is to say, all polynomials (which by definition are finite) which are defined over an algebraically closed field (complex numbers being one such example) have roots in that algebraically closed field. And if one "imaginary" number is a solution, so is its conjugate.
Basically, the complex numbers are a different beast than real numbers, although, under an appropriate isomorphism, R^2 is the same as C.