Complex Analysis studies functions of a complex variable, focusing on holomorphic functions, contour integration, and properties like analyticity and conformal mappings.

Metric Spaces provide a framework for distance and topology, defined by a metric satisfying non-negativity, symmetry, and the triangle inequality.

They connect through metric structures in C, such as the Euclidean and Poincaré metrics, which are essential in understanding function behavior and convergence in complex analysis.