mathwonk said:do you see how this implies the fundamental theorem of algebra?
As i understand it, this theorem states that any polynome can be factored by using complex numbers. There is always a complex root.
The fact that the windingnumber is non-zero implies that the origin is always a part of the disc, right ? Now, this means that any function with winding number non-zero must cross the horizontal x axis and it must have roots in those points. Is this correct ?