In mathematics, the complex squaring map, a polynomial mapping of degree two, is a simple and accessible demonstration of chaos in dynamical systems. It can be constructed by performing the following steps: 1. * Choose any complex number on the unit circle whose argument (angle) is not a rational multiple of π, 2. * Repeatedly square that number. This repetition (iteration) produces a sequence of complex numbers that can be described alone by their arguments. Any choice of starting angle that satisfies (1) above will produce an extremely complicated sequence of angles, that belies the simplicity of the steps. It can be shown that the sequence will be chaotic, i.e. it is sensitive to the detailed choice of starting angle. (Wikipedia).
From playlist Complex Multiplication
Complex Multiplication Sqrt(3) + i
From playlist Complex Multiplication
Complex Power: (1 + i sqrt(3))^3
From playlist Complex Multiplication
Dividing Complex Numbers Example
Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Complex Numbers
Complex Numbers in Trigonometric Form
This video explains how to write complex numbers in trigonometric form. http://mathispower4u.wordpress.com/
From playlist Complex Numbers
From playlist Complex Multiplication
ComplexMultiplication 1/3 - i/3
From playlist Complex Multiplication
Visualizing simple complex functions -- Complex Analysis 3
Mathematica Notebook: https://bit.ly/3t0ONEg ⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.yout
From playlist Complex Analysis
Digression: The cotangent complex and obstruction theory
We study the cotangent complex more in depth and explain its relation to obstruction theory. As an example we construct the Witt vectors of a perfect ring. This video is a slight digression from the rest of the lecture course and could be skipped. Feel free to post comments and questions
From playlist Topological Cyclic Homology
Duality In Higher Categories II by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Part I: Complex Variables, Lec 3: Conformal Mappings
Part I: Complex Variables, Lecture 3: Conformal Mappings Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Calculus of Complex Variables
Higher algebra 4: Derived categories as ∞-categories
In this video, we construct the ∞-categorical refinement of the derived category of an abelian category. This is the fourth video in our introduction to ∞-categories and Higher Algebra. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA
From playlist Higher Algebra
L^2 geometry of moduli spaces of vortices and lumps (Lecture 1) by James Martin Speight
PROGRAM VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual field the
From playlist Vortex Moduli - 2023
Mod-02 Lec-19 Special Techniques III
Electromagnetic Theory by Prof. D.K. Ghosh,Department of Physics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Electromagnetic Theory
Complex Analysis - Part 5 - Total Differentiability in ℝ²
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.
From playlist Complex Analysis
Graphs in the Complex Plane (1 of 3: Perpendicular bisector - visual method)
More resources available at www.misterwootube.com
From playlist Using Complex Numbers
Part I: Complex Variables, Lec 2: Functions of a Complex Variable
Part I: Complex Variables, Lecture 2: Functions of a Complex Variable Instructor: Herbert Gross View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Calculus Revisited: Calculus of Complex Variables