A conformal mapping is a function between domains that preserves angles and the shapes of infinitesimal figures at each point, even as it may distort their sizes. | Mathematical Muse

Conformal mapping is a powerful technique in complex analysis that involves transforming one region of the complex plane into another in a way that preserves angles. This means that if two curves intersect at a certain angle in the original plane, their images under the mapping will intersect at the same angle in the new plane. Conformal maps are generally defined by functions that are holomorphic and have nonzero derivatives, and they are widely used to simplify difficult geometric or physical

Conformal mapping is a tool in complex analysis that focuses on transformations which preserve angles and the local shape of small figures. In simple terms, it means that if two curves meet at a certain angle in one plane, they will meet at the same angle after the transformation in another plane. While the shapes are preserved locally, their size and overall layout can change dramatically. This makes conformal maps useful in physics and engineering, especially for problems involving fluid flow,