Complex-Valued Functions
Definition: Complex-Valued Function
A complex-valued function on a set is a function from to the set of the complex numbers.
Definition: Real Part
The real part of is the real-valued function which, for each , returns the real part of .
Definition: Imaginary Part
The imaginary part of is the real-valued function which, for each , returns the imaginary part of .
Operations with Complex-Valued Functions
Definition: Function Operations
Let and be Complex-Valued Functions.
- The sum of and is the function defined as
- The product of and is the function defined as
- The quotient of and is the function defined as