3D Representations of Complex Logarithms

This project generates 3D graphs, based on the logarithms of complex numbers. By writing a complex number in the form re^ia where r is the modulus of the complex number and a is the angle from the real plane, it is easy to take the logarithm of that complex number.

Log(z) = log(re^ia) = log(r) + log(e^ia) = log(r) + ia

The domain must be restricted because the function is periodic, since adding multiples of 2Pi gives the same result. Therefore the graphs generated show a single branch, and do not represent the entire function. Currently, by changing the num_levels variable you can stack branches.

Getting Started

These instructions will help you to get you a copy of the project running on your local machine.

Prerequisites

You will need these python modules to be able to run the project.

matplotlib - pip install matplotlib
numpy - pip install numpy

Installing

Clone this repository using terminal:

git clone https://github.com/LucasBN/Complex-Logarithms.git

To run the program open the cloned repository in terminal and type:

python main.py

Examples

The imaginary part over the complex plane:

The real part over the complex plane:

The imaginary part over the complex plane (two branches):

Creating your own plots

To plot your own function over the complex plane, create a function that returns a value for z given a complex number. (See example functions.)

Once you have created your function, make sure to assign the zs variable to its return value, by changing:

zs[xi,yi] = complex_log_real(z)

To:

zs[xi,yi] = new_zs_function(z)

Authors

• Lucas BN - Initial work

Acknowledgments

• 3blue1brown
• Xander Gouws