Squaring Function 4

Try a few more freehand traces. Move the square, circle and line segment to different places and orientations on the plane, then trace them with "Z" and see what happens to Z^2. This should start to give you a good idea of what the image of various regions in the plane is, under the complex squaring function.

1. What happens to a circle that has the origin in its interior (but not at the center?)

2. What happens to a line segment through the origin?

3. What happens to a line segment that is parallel to the x-axis? y-axis? other?

Dave Matthews, April 18, 2007, Created with GeoGebra