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
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