Complex Numbers Have More Uses Than You Think

Complex numbers are often seen as a mysterious or "advanced" number system mainly used for solving similarly mysterious or "advanced" problems. But really, once you get used to them, they're really an elegant and (ironically) simple mathematical tool with application to more down-to-earth problems besides Quantum Mechanics or advanced Differential Equations or something. Let's see what these numbers can do! Want to support future videos? Become a patron at https://www.patreon.com/morphocular Thank you for your support! =Chapters= 0:00 - Intro 1:45 - Complex number basics 3:31 - Interpreting complex number multiplication 7:55 - Angular velocity 10:42 - Calculating angular velocity using complex numbers 15:18 - Interpreting the formula 17:59 - More uses of complex numbers 19:48 - Special announcement! =============================== CREDITS The music tracks used in this video are (in order of first appearance): "Dream Escape", "Checkmate", "Orient", "Rubix Cube", "Frozen in Love" The track "Rubix Cube" comes courtesy of Audionautix.com =============================== The animations in this video were mostly made with a homemade Python library called "Morpho". If you want to play with it, you can find it here: https://github.com/morpho-matters/morpholib