Conformal mappings are mathematical functions that preserve angles and the local shape of small figures. They are used in complex analysis to transform one shape into another while maintaining the structure of the angles between curves. This property makes them valuable in various fields, including fluid dynamics and electrical engineering. These mappings are often represented using complex numbers, where the transformation can be visualized on the complex plane. A common example of a conformal mapping is the Riemann mapping theorem, which states that any simply connected open subset of the complex plane can be mapped conformally to the unit disk.