## Chapter 13CONFORMAL REPRESENTATION

Plus ça change, plus c’est la même chose.

**ALPHONSE KABR, ***Les Guépes,* 1849

### 13·01. Conditions for conformai mapping.

Let *ζ* and *z* be two complex variables related by

where *f*(*ζ*) is an analytic function. Then if *ζ* moves along a curve in the plane of *ξ*, *η, z* will move along a curve in the plane of *x*, *y.* Every value of *ζ* that *f*(*ζ*) is defined for will identify a point in the *x, y* plane, and conversely if the inverse function exists for a value of *z* a value of *ζ* will be identified. Thus (1) can be regarded as a *transformation*, enabling us to map at least a part of the *ξ, η* plane on the *x*, *y* plane and conversely.

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