Complex analysis is usually called the theory of functions of a complex variable, is the branch of mathematics examining functions of complex numbers. It is widely used not only in many branches of mathematics, such as the number theory and applied mathematics, but also in physics. Complex analysis in particular deals with the analytic functions of complex variables (or, more generally, meromorphic functions). The basic perceptions of complex analysis are often presented by extending the elementary real functions (e.g., exponentials, logarithms, and trigonometric functions) into the complex domain.

Among the numerous areas of study in complex analysis are the following:

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