# Conformal mappings

Chapter

## Abstract

Let *z*(*t*) = *x*(*t*) + *≀y*(*t*), *a* ≤ *t* ≤ *b*, be a path. We suppose throughout this chapter that *z*′(*t*) ≠ 0 for all *t*. Let *f* be defined in a neighborhood of a point *z* _{0} ∈ ℂ. *f* is conformal at *z* _{0} if *f* preserves angles at *z* _{0}, for any two paths *P* _{1} and *P* _{2} intersecting at *z* _{0} the angle from *P* _{1} to *P* _{2} at *z* _{0}, the angle oriented counterclockwise from the tangent line of *P* _{1} at *z* _{0} to the tangent line of *P* _{2} at *z* _{0}, is equal to angle between *f*(*P* _{1}) and *f*(*P* _{2}). The function *f* is conformal in a region *O* if it is conformal at all points from *O*.

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## Copyright information

© Springer Science+Business Media Dordrecht 1999