Complex Mapping: [math]f(z)=z/|z|^2[/math]. [br][br]1. The point Z is an arbitrary complex number. Notice the behaviour of [math]W=f(Z)=Z/|Z|^2[/math] when Z is moved.[br][br]2. The points [math]Z_1[/math] and [math]Z_2[/math] are defined on a line and a conic, respectively. Notice the behaviour of [math]W_1=f(Z_1)=Z_1/|Z_1|^2[/math] and [math]W_2=f(Z_2)=Z_2/|Z_2|^2[/math] when [math]Z_1[/math] and [math]Z_2[/math] are moved.[br][br]To move [math]Z_1[/math] and [math]Z_2[/math] simultaneously click on the Animate button.

What happens if Z approches to the origin (0,0)?