🚀 LEVEL UP TO SENIOR:Unlock 500+ Advanced Practical Challenges & Exercises.
🎓 COURSERA PARTNER:Earn professional Google, Meta, and IBM certificates to supercharge your resume.
REFERENCEpython

python Documentation

LOADING ENGINE...

Complex Numbers

AI & DATA SCIENCE // complex-numbers

A complex number is Python's built-in type for numbers with a real and an imaginary part, written as a real component plus a j suffix for the imaginary component.

Syntax

z = 3 + 4j
z.real
z.imag
abs(z)

Deep Dive Course

Python has native syntax for complex numbers: writing 3 + 4j creates one directly, using j instead of the mathematical i, following the electrical-engineering convention, and the type supports the usual arithmetic operators, plus .real and .imag attributes to pull out each component. abs() on a complex number returns its magnitude rather than a sign-stripped value, since complex numbers aren't ordered.

1Understanding Complex Numbers

Python has native syntax for complex numbers: writing 3 + 4j creates one directly, using j instead of the mathematical i, following the electrical-engineering convention, and the type supports the usual arithmetic operators, plus .real and .imag attributes to pull out each component. abs() on a complex number returns its magnitude rather than a sign-stripped value, since complex numbers aren't ordered.

💡

Complex numbers rarely show up in everyday scripting — they're mainly used in scientific/engineering code, like signal processing, electrical engineering, and certain numerical algorithms, often via libraries like NumPy, which builds on this same complex type.

editor.html
z = 3 + 4j
print(z.real, z.imag)
print(abs(z))
localhost:3000

2Practical Example

Here is a real-world application of Complex Numbers showing how it is used in production Python code.

editor.html
z1 = 2 + 3j
z2 = 1 - 1j
print(z1 + z2)
print(z1 * z2)
localhost:3000

3Best Practices

Follow these guidelines when working with Complex Numbers:

1. Use the built-in complex type or complex() constructor instead of modeling real/imaginary parts as a manual tuple

2. Access .real and .imag instead of parsing the number's string representation

3. Reach for NumPy's complex arrays instead of Python's plain complex type when doing bulk numerical work

⚠️

Tip: Complex numbers rarely show up in everyday scripting — they're mainly used in scientific/engineering code, like signal processing, electrical engineering, and certain numerical algorithms, often via libraries like NumPy, which builds on this same complex type.

editor.html
z = 3 + 4j
print(z.real, z.imag)
print(abs(z))
localhost:3000

Examples

Example 01Basic Usage
z = 3 + 4j
print(z.real, z.imag)
print(abs(z))
Example 02Advanced Example
z1 = 2 + 3j
z2 = 1 - 1j
print(z1 + z2)
print(z1 * z2)

Best Practices

  • Use the built-in complex type or complex() constructor instead of modeling real/imaginary parts as a manual tuple
  • Access .real and .imag instead of parsing the number's string representation
  • Reach for NumPy's complex arrays instead of Python's plain complex type when doing bulk numerical work

Interview Question

Why does Python use j instead of i for the imaginary unit in complex number literals?

Hint: Think about which fields commonly use complex numbers and their notation conventions.

Python borrows the j notation from electrical engineering, where i is already reserved for electric current, so engineers historically use j for the imaginary unit instead. Python's complex literal syntax follows that convention rather than the pure-mathematics i.

Exercises

MediumPractice using Complex Numbers in a real scenario.
View Solution
z = 3 + 4j
print(z.real, z.imag)
print(abs(z))

Frequently Asked Questions

Why does Python use j instead of i for the imaginary unit in complex number literals?

Python borrows the j notation from electrical engineering, where i is already reserved for electric current, so engineers historically use j for the imaginary unit instead. Python's complex literal syntax follows that convention rather than the pure-mathematics i.

Related Functions

floatsabs()numpy complex arrays