Examples for

# Complex Analysis

Complex analysis is the field of mathematics dealing with the study of complex numbers and functions of a complex variable. Wolfram|Alpha's authoritative computational ability allows you to perform complex arithmetic, analyze and compute properties of complex functions and apply the methods of complex analysis to solve related mathematical queries.

Complex Numbers

Analyze properties of functions of a complex variable or perform basic arithmetic on, find roots of or apply functions to complex numbers.

#### Apply functions to complex numbers:

More examples
Poles

Locate poles of a complex function within a specified domain or within the entire complex plane.

#### Locate poles in a specified domain:

Complex Functions

Plot functions of a complex variable or compute and analyze their properties.

#### Determine the harmonic conjugate:

Residues

Compute the residues of functions in the complex plane at a point or within a specified region.

### RELATED EXAMPLES

• Calculus & Analysis
• Differential Equations
• Quaternions
• ### RELATED WOLFRAM RESOURCES

• Explore Complex Analysis at Wolfram MathWorld
• Wolfram Complex Numbers Guide Page
• Wolfram Functions of Complex Variables Guide Page
• Wolfram Tutorial on Expressions Involving Complex Variables
• Riemann Surfaces

Compute and visualize Riemann surfaces for complex functions.