- 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).

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