Complex Number Library

A comprehensive Python library for performing operations on complex numbers using tuple representations without using the python complex numbers data type.

Features

The library provides 8 essential complex number operations:

• Addition - Add two complex numbers
• Subtraction - Subtract two complex numbers
• Multiplication - Multiply two complex numbers
• Division - Divide two complex numbers
• Modulus - Calculate the magnitude of a complex number
• Conjugate - Find the complex conjugate
• Phase - Calculate the argument (angle) of a complex number
• Coordinate Conversion - Convert between Cartesian and polar representations

Getting Started

Prerequisites

• Python 3.6 or higher
• No external dependencies required (uses only Python standard library)

Installation

1. Clone the repository:

git clone https://github.com/AnderssonProgramming/complex-number-library.git
cd complex-number-library

2. The library is ready to use - no installation required!

Usage

Import the library and start using complex number operations:

from ComplexNumberLibrary import *

# Define complex numbers as (real, imaginary) tuples
z1 = (3, 4)  # Represents 3 + 4i
z2 = (1, 2)  # Represents 1 + 2i

# Basic operations
sum_result = add_complex(z1, z2)          # (4, 6)
diff_result = subtract_complex(z1, z2)    # (2, 2)
product = multiply_complex(z1, z2)        # (-5, 10)
quotient = divide_complex(z1, z2)         # (2.2, -0.4)

# Advanced operations
magnitude = modulus_complex(z1)           # 5.0
conjugate = conjugate_complex(z1)         # (3, -4)
angle = phase_complex(z1)                 # 0.9272952180016122

# Coordinate conversion
polar_form = cartesian_to_polar(z1)       # (5.0, 0.9272952180016122)
cartesian_form = polar_to_cartesian(polar_form)  # (3.0, 4.0)

Running the Tests

The project includes comprehensive unit tests using Python's unittest framework.

To run all tests:

python TestComplexNumberLibrary.py

Expected output:

...........
----------------------------------------------------------------------
Ran 11 tests in 0.010s

OK

Test Coverage

The test suite includes:

• 11 test methods covering all 8 functions
• Multiple test cases per function (minimum 2 per function as required)
• Edge cases: zero division, zero values, negative numbers
• Mathematical properties: modulus multiplication property, conjugate properties
• Round-trip conversions: Cartesian ↔ Polar conversions

API Reference

Core Operations

add_complex(z1, z2)

Adds two complex numbers.

• Parameters: z1, z2 - Complex numbers as (real, imaginary) tuples
• Returns: Sum as (real, imaginary) tuple

subtract_complex(z1, z2)

Subtracts z2 from z1.

• Parameters: z1, z2 - Complex numbers as (real, imaginary) tuples
• Returns: Difference as (real, imaginary) tuple

multiply_complex(z1, z2)

Multiplies two complex numbers.

• Parameters: z1, z2 - Complex numbers as (real, imaginary) tuples
• Returns: Product as (real, imaginary) tuple

divide_complex(z1, z2)

Divides z1 by z2.

• Parameters: z1, z2 - Complex numbers as (real, imaginary) tuples
• Returns: Quotient as (real, imaginary) tuple
• Raises: ZeroDivisionError if z2 is zero

Mathematical Functions

modulus_complex(z)

Calculates the modulus (magnitude) of a complex number.

• Parameters: z - Complex number as (real, imaginary) tuple
• Returns: Modulus as float

conjugate_complex(z)

Finds the complex conjugate.

• Parameters: z - Complex number as (real, imaginary) tuple
• Returns: Conjugate as (real, -imaginary) tuple

phase_complex(z)

Calculates the phase (argument) in radians.

• Parameters: z - Complex number as (real, imaginary) tuple
• Returns: Phase angle as float (in radians)

Coordinate Conversion

cartesian_to_polar(z)

Converts from Cartesian to polar coordinates.

• Parameters: z - Complex number as (real, imaginary) tuple
• Returns: Polar form as (magnitude, phase) tuple

polar_to_cartesian(polar_z)

Converts from polar to Cartesian coordinates.

• Parameters: polar_z - Complex number as (magnitude, phase) tuple
• Returns: Cartesian form as (real, imaginary) tuple

Project Structure

complex-number-library/
├── ComplexNumberLibrary.py      # Main library implementation
├── TestComplexNumberLibrary.py  # Comprehensive unit tests
├── README.md                    # Project documentation
├── LICENSE                      # GPL-3.0 license
└── .gitignore                   # Git ignore rules

Mathematical Representation

This library uses tuples to represent complex numbers:

• Cartesian form: (real, imaginary) where the complex number is real + imaginary*i
• Polar form: (magnitude, phase) where the complex number is magnitude * e^(i*phase)

Built With

• Python 3 - Core programming language
• Math module - For trigonometric and mathematical functions
• Unittest - Testing framework

Contributing

1. Fork the repository
2. Create your feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'feat: add some amazing feature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

Please use conventional commit messages (feat, fix, docs, test, chore, etc.).

Versioning

We use SemVer for versioning. For the versions available, see the tags on this repository.

Authors

• Andersson Programming - Initial work - AnderssonProgramming

License

This project is licensed under the GPL-3.0 license - see the LICENSE file for details.

Acknowledgments

• Python Software Foundation for the excellent unittest framework
• Mathematical foundations from complex analysis theory
• Academic requirements that inspired this implementation