"Complex analysis" is a term used in mathematics to describe the study of functions that are based on complex numbers. It is a complex and detailed field that requires a depth of knowledge and skill. There are several synonyms that are used interchangeably with "complex analysis" such as "complex variables", "complex function theory", and "analytic function theory". These all refer to the same mathematical principles that involve the study of functions that are defined on a complex plane. Regardless of which term is used, each one ultimately refers to this complex field that is essential in understanding the behavior of various mathematical functions.