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 tool in complex analysis that refers to functions that locally preserve angles and the shapes of infinitesimally small figures. These mappings are typically defined by analytic functions with non-zero derivatives, which ensures that the local geometry of a shape is maintained, though the size may be distorted. Conformal maps are especially useful in solving problems involving fluid flow, electromagnetism, and complex potential theory, as they allow complicated dom