# Complex Numbers?

Complex Numbers, I just don't understand what they are supposed to represent. I understand how they are used, to some degree in solving equations etc. but the definitions leave me clueless. The idea that they "extend the idea of the one-dimensional number line to the two-dimensional complex plane" sort of makes sense. If each number consists of a real part and an imaginary part (a+bi etc.), then starting from a number-line representing the real number a, you can extend a y axis to represent i. But what does that really mean?? What would be a good visual explanation of this concept?