# 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 variable?

Summarize this article for a 10 year 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, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.^{[1]}

This article includes a list of general references, but it lacks sufficient corresponding inline citations. (March 2021) |

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*.
The concept can be extended to functions of several complex variables.