Cookbooks
Python
Chapter 3. Numbers
Working with complex numbers

Python:
Working with complex numbers

How to:

Python has built-in support for complex numbers. Here’s how you can play with them:

# Creating complex numbers
z = 4 + 5j
print(z)  # Output: (4+5j)

# Accessing real and imaginary parts
print(z.real)  # Output: 4.0
print(z.imag)  # Output: 5.0

# Complex arithmetic
w = 1 - 2j
print(z + w)  # Output: (5+3j)
print(z - w)  # Output: (3+7j)
print(z * w)  # Output: (14+2j)
print(z / w)  # Output: (-3.6+1.2j)

# Modulus (absolute value)
print(abs(z))  # Output: 6.4031242374328485

# Conjugate of a complex number
print(z.conjugate())  # Output: (4-5j)

Deep Dive

Complex numbers were first conceptualized by Gerolamo Cardano in the 16th century. Python, among other programming languages, treats complex numbers as first-class citizens. This means they’re built into the language, with easy-to-use features, avoiding the need for importing external libraries for basic operations.

However, for heavy numerical computations, Python has a library called cmath, which is specifically for complex numbers. It has additional functions like exp, log, and trigonometric operations.

When Python isn’t enough, you might turn to libraries like NumPy, especially for array operations involving complex numbers. NumPy provides optimized and vectorized operations that are crucial for performance in numerical computing.

See Also

Check out these resources to learn more:

Rounding numbers