This worksheet is meant to help explore how a particular mapping transforms the plane. The shape with vertices [i]A'[/i]-[i]D'[/i] below is the image of the rectangle [i]ABCD[/i] under the rational mapping [math]w: \mathbb{C} \rightarrow \mathbb{C} [/math]. The grid lines in the image correspond to a grid within the preimaged rectangle, where [i]incr[/i] is the width of the preimage's grid squares.
Reposition the preimage rectangle by moving the point [i]A[/i]. The sliders [i]choose vert[/i] and [i]choose flat[/i] let you highlight particular grid lines in the preimage along with their corresponding images.