Here is a picture of the function z^3 - 2z + 2. The black spots are zeros of this function. Notice that there is a full spectrum of colors around each zero. It looks like there is a lot more red near the zeros. What will the picture look like if you zoom in closer to a zero? What if the shading was removed? (i.e. how would the colors be spaced? How much will the colors be rotated?) If a polynomial had a zero of order 3, what would the picture look like near the zero? Where are the zeros of the derivative on this picture? Can you describe what happens near the zeros of the derivative?