The Complex Squaring Function

Drag the blue points to see the effect of inverting the complex number a. The checkboxes show different shapes. The "before" shape is filled in, and is traced by the blue point P. The "after" shape is not filled, and is traced by P'.
This function finds the square of a complex number z=x+iy. It can be computed by multiplying out (x+iy)^2. The absolute value of z^2 is the square of the absolute value of z. The angle of z^2 is twice the angle of z.