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Complex analysis

branch of mathematics studying functions of a complex variable

Complex analysis is the area of mathematical analysis that looks at functions on the complex numbers. It has a wide range of uses, including algebraic geometry and analytic number theory, and areas of physics, such as string theory and quantum mechanics. Augustin-Louis Cauchy is normally credited with founding complex analysis, building on the work of Gauss and Euler. Other mathematicians that made significant advances in this field include Riemann and Weierstrass.