Complex Functions
A complex function is one in which the independent variable and the dependent variable are both complex numbers. More precisely, a complex function is a function whose domain and range are subsets of the complex plane.
For any complex function, both the independent variable and the dependent variable may be separated into real and imaginary parts:
- and
- where and are real-valued functions.
In other words, the components of the function f(z),
- and
can be interpreted as real-valued functions of the two real variables, x and y.
The basic concepts of complex analysis are often introduced by extending the elementary real functions (e.g., exponentials, logarithms, and trigonometric functions) into the complex domain.
Read more about this topic: Complex Analysis
Famous quotes containing the words complex and/or functions:
“Power is not an institution, and not a structure; neither is it a certain strength we are endowed with; it is the name that one attributes to a complex strategical situation in a particular society.”
—Michel Foucault (1926–1984)
“Let us stop being afraid. Of our own thoughts, our own minds. Of madness, our own or others’. Stop being afraid of the mind itself, its astonishing functions and fandangos, its complications and simplifications, the wonderful operation of its machinery—more wonderful because it is not machinery at all or predictable.”
—Kate Millett (b. 1934)