This video visualizes the complex function f(z) = 1/z using domain coloring, stereographic projection and the Riemann sphere.
At first, the transformation looks chaotic: the complex plane twists, points near zero fly outward, and far-away points move toward zero. But once we look at the extended complex plane as a sphere, the whole picture becomes much simpler.
Using stereographic projection, we see that the map z → 1/z corresponds to a simple 180-degree rotation of the Riemann sphere around the x-axis.
So what looks complicated on the plane becomes beautifully simple on the sphere.
This is our first step towards the Möbiustransformation :) thx bye
#StereographicProjection #ComplexAnalysis #RiemannSphere #Mobiustransformation #DomainColoring #StereographicProjection # #MathVisualization #ComplexNumbers #VisualMath #Manim #MathAnimation
