The Extended Complex Plane (Riemann Sphere)
This video introduces the extended complex plane, obtained by adjoining the symbol "infinity" to the complex plane. Then we extend the stereographic projection to take values on the whole sphere (including the north pole) to obtain a bijection with the extended complex plane. The majority of the video goes through the proof that the stereographic projection takes circles on the sphere to circles (or lines) in the extended complex plane.

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The Cross Ratio

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What if we define 1/0 = ∞? | Möbius transformations visualized

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The most beautiful formula not enough people understand

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Introduction to Riemann Sphere (A visualized approach)
![Imaginary Numbers Are Real [Part 13: Riemann Surfaces]](https://i.ytimg.com/vi/4MmSZrAlqKc/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLAVizRd1BrVExexb0yrycoKrT3PeQ)
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Imaginary Numbers Are Real [Part 13: Riemann Surfaces]

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The Stereographic Projection onto the Extended Complex Plane

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What do complex functions look like? | Essence of complex analysis #4

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The shocking connection between complex numbers and geometry.

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Complex Analysis | Unit 1 | Lecture 18 | Stereographic Projection

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Visualizing the 4d numbers Quaternions

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The Riemann Hypothesis, Explained

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The intuition and implications of the complex derivative

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B. Riemann and the complex sphere | Sociology and Pure Mathematics | N J Wildberger

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The 5 ways to visualize complex functions | Essence of complex analysis #3

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When Math Isn’t Based in Reality

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Understanding Lagrange Multipliers Visually

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Complex Numbers Have More Uses Than You Think
![You’ll stop using ChatGPT after listening to this | Jonathan Pageau [ARC 2026]](https://i.ytimg.com/vi/yZUuKzDQSsI/hqdefault.jpg?sqp=-oaymwEjCNACELwBSFryq4qpAxUIARUAAAAAGAElAADIQj0AgKJDeAE=&rs=AOn4CLAXTozuIcoGA_3ys1pkvHYXgL8C4Q)
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You’ll stop using ChatGPT after listening to this | Jonathan Pageau [ARC 2026]

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The Boundary of Computation

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