The hue represents the function argument, while the brightness represents the magnitude. For the class of functions often called “complex analytic”, see Holomorphic function. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that real and complex analysis rudin pdf solutions functions of complex numbers.

By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. Complex analysis is one of the classical branches in mathematics, with roots in the 19th century and just prior. Important mathematicians associated with complex analysis include Euler, Gauss, Riemann, Cauchy, Weierstrass, and many more in the 20th century.