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