Conformal Map: A Definition


DEFINITION:
A map is conformal at a point P in its domain if it preserves the measures of all angles at the point P.
(note: this does not mean that the map must send P to itself).
DEFINITION:
Let f be a map from C → C. f is conformal if it is conformal at all points.

A LOOK AT ANGLE PRESERVATION;
Let f be a conformal map from C → C, and S1 and S2 represent two curves in C which intersect at a complex point P.
t1 = tangent line of S1 at P.
t2 = tangent line of S2 at P.
θ = angle from t1 to t2.



Now we apply the conformal map f to S1 and S2 to yield f(S1) and f(S2), and let t1' and t2' be the corresponding tangent lines of f(S1) and f(S2) through the new point of intersection P'.

f

The angle from t1 to t2 is the same as the angle from t1' to t2' (including orientation).


HOME