Question

What is meant by conformal mapping in complex analysis?

Answer 1

A conformal mapping, also called a conformal map, conformal transformation, angle-preserving transformation, or biholomorphic map, is a transformation that preserves local angles. An analytic function is conformal at any point where it has a nonzero derivative. Conversely, any conformal mapping of a complex variable which has continuous partial derivatives is analytic. Conformal mapping is extremely important in complex analysis, as well as in many areas of physics and engineering.

A mapping that preserves the magnitude of angles, but not their orientation is called an isogonal mapping.

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