z
exp(z)
The following illustrates the general form of various mappings in the complex plane. The mappings are applied to part of a unit disk centered at the origin as shown on the left hand side. The circle is filled with rays from the origin and arcs centered about the origin. A series of coloured rays further illustrate the mapping orientation.
z
|
exp(z)
|
z
|
log(z)
|
z
|
sqrt(z)
|
z
|
asin(z)
|
z
|
acos(z)
|
z
|
atan(z)
|
z
|
sin(z)
|
z
|
cos(z)
|
z
|
tan(z)
|
z
|
sinh(z)
|
z
|
cosh(z)
|
z
|
tanh(z)
|
z
|
z2
|
z
|
z2 + z
|
z
|
1 / (z + 1)
|
z
|
(z - 1) / (z + 1)
|
z
|
(z2 - 1) / (z2 + 1)
|
z
|
(z - a) / (z + b)
|
z
|
(z2 + z - 1) / (z2 + z + 1)
|
z
|
(z2 + z + 1) / (z + 1)
|
|
Mapping software written by myself, interface using the FORMs
library, rendering with GeomView, conducted on a SGI Indigo-2.
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