> What? You can take the square root of a negative? Since when? How can you do that?

You can't take the square root of a negative and remain within the set of real numbers. There is, however, another number line that could be considered perpendicular to the real number line, that represents imaginary numbers. 'i' is used to denote the square root of -1. That's all the definition 'i' has -- it's a purely theoretical concept yet one that has proved to have useful application in, for example, electronics. The square root of -9 would be 3i. Complex numbers include both a real and imaginary term, for example, 5 + 4i. Powers of imaginary numbers are interesting: i^2 = -1. i^3 = -i. i^4 = 1. i^5 = i. Etc.