Complex Coordinates in Real Geometry

Complex numbers usually appear solely as a way to solve polynomial equation. Here, I want to show you what that means for doing geometry.

This video complements my other one about perspective drawings: https://www.youtube.com/watch?v=mTw3o8-xMIo
While they can be understood completely independent from one another, they cover similar ideas from different perspective. It's definitely beneficial to watch both.

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Resources, references & further reading material:

Animations were made with CindyJS:
https://cindyjs.org/

Richter-Gebert, J. (2011) Perspectives in Projective Geometry:
https://link.springer.com/book/10.1007/978-3-642-17286-1

Homogeneous Coordinates on Wikipedia:
https://en.wikipedia.org/wiki/Homogeneous_coordinates

Conic sections on Wikipedia:
https://en.wikipedia.org/wiki/Conic_section

I & J on Wikipedia:
https://en.wikipedia.org/wiki/Circular_points_at_infinity

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Chapters:

[00:00] Opening
[00:34] Homogeneous Coordinates
[05:03] Lines
[08:57] Conics
[13:28] Complex Numbers
[14:42] Circles
[17:42] Beyond Circles

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Music:

spacedust by airtone (c) copyright 2022 Licensed under a Creative Commons Attribution (3.0) license. http://dig.ccmixter.org/files/airtone/64741