complex

The built-in complex data type provides support for complex numbers, which are essential in mathematical computations involving two-dimensional vector arithmetic, sound frequency analysis, and fractal generation. Here’s a quick example of creating a complex number using literals and accessing its values:

Python 
>>> z = 3 + 2j
>>> z.real
3.0
>>> z.imag
2.0

complex Constructors

Python Syntax 
complex(real=0, imag=0)
complex(string)

Arguments

Argument Description Default Value
real The real component of the complex number. 0
imag The imaginary component of the complex number. 0
string A string representation of a complex number, which can include both real and imaginary components Required argument

Return Value

  • Returns a Python complex object

complex Examples

Creating an empty instance of a complex number:

Python 
>>> z = complex()
>>> z
0j

Creating instances using literals:

Python 
>>> x = 3 + 2j
>>> x
(3+2j)
>>> y = 3.14 + 0j
>>> y
(3.14+0j)
>>> z = 0 + 2.71j
>>> z
2.71j

Creating an instance using the class constructor:

Python 
>>> z = complex(3, 2)
>>> z
(3+2j)

Accessing the components of a complex number:

Python 
>>> z.real
3.0
>>> z.imag
2.0

complex Methods

Method Description
.conjugate() Returns the complex conjugate of the number

complex Common Use Cases

The most common use cases for the complex data type include:

  • Performing mathematical calculations involving complex numbers
  • Representing two-dimensional vectors
  • Conducting frequency analysis in sound engineering
  • Generating fractals such as the Mandelbrot set

complex Real-World Example

Say that you need to calculate the distance between two points on the complex plane, representing them as complex numbers:

Python 
>>> point1 = complex(1, 2)
>>> point2 = complex(4, 6)
>>> distance = abs(point2 - point1)
>>> distance
5.0

In this example, complex numbers allow us to treat points as vectors, and the abs() function computes the distance between these points, showcasing the practical use of complex numbers in geometry.

Simplify Complex Numbers With Python

Tutorial

Simplify Complex Numbers With Python

In this tutorial, you'll learn about the unique treatment of complex numbers in Python. Complex numbers are a convenient tool for solving scientific and engineering problems. You'll experience the elegance of using complex numbers in Python with several hands-on examples.

intermediate python

For additional information on related topics, take a look at the following resources:

By Leodanis Pozo Ramos • Updated Dec. 6, 2024 • Reviewed by Dan Bader
Python’s Built-in Data Types Share Feedback