cover image

Complex analysis

Branch of mathematics studying functions of a complex variable / From Wikipedia, the free encyclopedia

Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Complex analysis?

Summarize this article for a 10 years old


Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, and particularly quantum mechanics. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.[citation needed]

As a differentiable function of a complex variable is equal to its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions).