"also (i, -2i) and (-i, 2i), whatever these complex thingys mean, I don't remember."

Every nth degree equation has n solutions. Some solutions may be double roots (i.e. (x-1)(x-1) = 0). The graph may only pass through the x-axis (where y = 0, which would be a solutions) less than n times. When this occurs, you get an imaginary solution, which is what i is.