Understanding The Complex Plane For High School скачать в хорошем качестве

Understanding The Complex Plane For High School

This video goes over the geometrical interpretation of multiplying complex numbers as rotation and scaling, and thus explains why the complex plane is drawn as a plane, with the imaginary axis perpendicular to the real axis. This video also covers the Cartesian and polar coordinates and form, as well as the exponential form, and where they come from. ------- TABLE OF CONTENTS 00:00 Intro 00:10 Multiplication as rotation and scaling 03:01 Square roots of positive numbers 04:53 Square roots of negative numbers 08:08 The complex plane 09:39 Polar coordinates 10:20 Cartesian coordinates & Cartesian form 11:47 Polar form & Principal argument 14:49 Exponential form 17:10 Bringing it all together 17:51 Next steps ------- CREDITS The scaling and rotation interpretation are nothing new; I primarily learnt it from the following series: 1. "Lockdown Math"    • Lockdown math   by ‪@3blue1brown‬ 2. "Imaginary Numbers Are Real"    • Imaginary Numbers are Real   by ‪@WelchLabs‬ I encourage those who are curious for more of the history and math beyond high school to check out these great series. Thank you for teaching me this interpretation; it has made complex numbers so much clearer and more beautiful. I thank my math teacher in high school for teaching complex numbers more generally. Thank you again to ‪@GrantSanderson‬ (3Blue1Brown) for videos on how to make better math explainers, such as    • Make math videos! | Summer of Math Exposit...   and    • Math's pedagogical curse | Grant Sanderson...  , and thank you too for first encouraging us to create math explainers. It has inspired me to do so finally. Thank you ‪@aarthificial‬ for creating Motion Canvas, which this video is primarily made with. Thank you to the Discord community for your help and encouragement, especially Hunter, Pihedron (    / @pihedron   ), and all others, both past and present. I would not have been able to do this without all your help and all the past questions and answers left in the server.