Conformal maps as sense preserving

[RichardJB]

Hi everyone,

Long time lurker on the forums here...lots of good reading to be had! This is not too much of a homework question rather than me just being curious about a certain property, although I thought I might as well post it here since other students will most likely find this helpful. Most complex analysis textbooks I've come across state that conformal mappings are sense and angle preserving (between curves). They readily prove the angle preserving part, but I've never actually seen a formal proof of why they preserve the sense of any simple curves. How is this usually accomplished?

This didn't initially bother me too much, and I just sort of accepted the fact, but I had to explain conformal mapping to a few university friends today and this got me thinking about this fact.

Thanks!

 

[micromass]

Well, in any proof that conformal mappings are angle-preserving, they prove that conformal mappings actually preserve oriented angles. An example of such a proof is ww.worldscibooks.com/etextbook/4836/4836_chap1_6.pdf

Now, this mean that the proofs show that orientation of the angles are being preserved. But this is of course thesame as saying that the mapping is sense-preserving...