"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."
The study of complex numbers and their functions, including complex derivatives, integrals, and series.
"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, 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."
"Complex analysis is particularly concerned with analytic functions of a complex variable (that is, holomorphic functions)."
"Complex analysis, traditionally known as the theory of functions of a complex variable…"
"Complex analysis… investigates functions of complex numbers."
"It is helpful in many branches of mathematics, including algebraic geometry…"
"…including the branches of hydrodynamics…"
"…engineering fields such as nuclear, aerospace, mechanical and electrical engineering."
"…analytic functions of a complex variable…"
"It is helpful in many branches of mathematics…"
"It is helpful in many branches of mathematics, including… applied mathematics."
"…use of complex analysis also has applications in engineering fields…"
"By extension, use of complex analysis also has applications in engineering fields…"
"…the theory of functions of a complex variable…"
"It is helpful in many branches of mathematics, including… number theory…"
"…hydrodynamics, thermodynamics, quantum mechanics, and twistor theory."
"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…"
"Complex analysis is particularly concerned with…"