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What does a complex function look like?

Join me as I explore the different ways we can visualize a complex function, to find which one deserves to be called their true graph. ================================================= 0:00 - Quick introduction 0:30 - Why can't we just plot a complex function? 1:45 - Mapping between 2 planes 2:35 - Grid mapping 3:07 - Reading a grid map 4:15 - The problem with grid mapping 5:35 - Colors to the rescue! 7:07 - Mapping hue and brightness 8:11 - Contour maps 8:43 - Domain coloring: z/(z^2 + 1) 10:07 - Domain coloring + contour lines 10:40 - Domain coloring: z^2 11:00 - Domain coloring: e^z 12:05 - Domain coloring: z^5 + z^2 12:30 - Domain coloring: tan(z) and (z-4i)/(z+4i) 13:20 - Going 3D 14:50 - |f(z)| + hue 16:20 - What is a graph? 18:12 - Projections and surfaces in 4D 18:53 - Graphing Re(f(z)) 19:45 - Re(f(z)) + hue ================================================= The bulk of the code I used can be found on github: [https://github.com/mathematimpa/compl...] CC atributions: Contour map of Mt St Helens Clarknova, CC BY-SA 3.0 [https://creativecommons.org/licenses/...], via Wikimedia Commons