Complex Map
A complex map is a map f:C->C. The following table lists several common types of complex maps.
map formula domain
complex
magnification f(z)=az a in R, a>0
complex
rotation f(z)=e^(itheta)z theta in R
complex
translation f(z)=z+a a in C
inversion f(z)=1/z
linear
fractional transformation f(z)=(az+b)/(cz+d) a,b,c,d in C
magnification+rotation f(z)=az a in C!=0
See also
Complex Magnification, Complex Rotation, Complex Translation, Linear Fractional Transformation, MapExplore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Complex Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplexMap.html