Complex Linear Mapping Diagram II: f(z) = Az
The complex linear function is crucial in understanding the complex derivative.
The Geometry of the magnification by leads to a cone in the mapping diagram with its vertex determined by , the twist that is connected to giving a swirl like curve on the cone that is close to a "geodesic" curve on the cone.
Move A and z# to change the parameter A and the point z#.
Click on the boxes to show mapping diagram arrows and/or mapping diagram "geodesic" curves on the magnification cone.
Change r on the slider to change the domain circle "|z| = r".