Complex Numbers

Iterated Functions
Fractals
L-Systems
Mandelbrot
Julia
Algorithmic Patterns
Symmetry
Published

May 2, 2024

Modified

May 17, 2025

Introduction

One of the most basic kinds of numbers we will need are, of course, Complex Numbers. But what are they?

Complex Planes: What am i?

Dude, what’s the square root of -1?? 🙀 🙀 🙀!! And, what can you do repeatedly to arrive at [−1,0]?

Wait, But Why?

  • Complex Numbers are very useful in handling “2D data” in a compact fashion
  • Complex Numbers help us to intuitively visualize, and implement, ideas such as rotation, scaling, and shadows, and projections.
  • The duality between rotating vectors and complex numbers is a very important concept.

References

  1. Working with Shadows. https://www.wikiwand.com/en/Map_projection
  2. Working with Fourier Series and Epicyles http://www.jezzamon.com/fourier/index.html and https://alex.miller.im/posts/fourier-series-spinning-circles-visualization/
  3. https://twitter.com/i/status/962449509782495232 https://codegolf.stackexchange.com/questions/36374/redraw-an-image-with-just-one-closed-curve
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Citation

BibTeX citation:
@online{2024,
  author = {},
  title = {\textless Iconify-Icon Icon=“tabler:math-Xy” Width=“1.2em”
    Height=“1.2em”\textgreater\textless/Iconify-Icon\textgreater{}
    {Complex} {Numbers}},
  date = {2024-05-02},
  url = {https://av-quarto.netlify.app/content/courses/MathModelsDesign/Modules/25-Geometry/20-ComplexNumbers/},
  langid = {en}
}
For attribution, please cite this work as:
“<Iconify-Icon Icon=‘tabler:math-Xy’ Width=‘1.2em’ Height=‘1.2em’></Iconify-Icon> Complex Numbers.” 2024. May 2, 2024. https://av-quarto.netlify.app/content/courses/MathModelsDesign/Modules/25-Geometry/20-ComplexNumbers/.