Mapping Circles by a Linear Fractional Transformation
Mapping Circles by a Linear Fractional Transformation
A linear fractional transformation (or Möbius transformation) in the complex plane is a conformal mapping that has the form , where , , , and are complex, with . The transformation transforms circles in the plane into circles in the plane, where straight lines can be considered to be circles of infinite radius.
w=f(z)=
az+b
cz+d
a
b
c
d
ad-bc≠0
f
z
w
In this Demonstration, the red circle is transformed into the blue circle of the form .
|z-|=r
z
0
|w-|=s
w
0