Complex Mapping [math]f(z)=\log (z)[/math]. The points [math]z_1[/math] and [math]z_2[/math] are defined on the blue circles and red segments, respectively. Here we consider the principal argument [math]-\pi< \Theta\leq \pi[/math]. [br] [br]Observe the behaviour of [math]w_1=\log (z_1)[/math] and [math]w_2=\log (z_2)[/math] when [math]z_1[/math] and [math]z_2[/math] are moved. You can also change the branch of the logarithm.

To move [math]z_1[/math] and [math]z_2[/math] simultaneously click on the Animate button. Drag the sliders to observe what happens to both graphs.