In mathematics, a complex line is a one-dimensional affine subspace of a vector space over the complex numbers. A common point of confusion is that while a complex line has dimension one over C (hence the term "line"), it has dimension two over the real numbers R, and is topologically equivalent to a real plane, not a real line. (Wikipedia).
From playlist Complex Analysis Made Simple
Complex Numbers as Points (1 of 4: Geometric Meaning of Addition)
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From playlist Complex Numbers
Dividing Complex Numbers Example
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From playlist Complex Numbers
Geometry of Complex Numbers (3 of 6: Real Arithmetic)
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From playlist Introduction to Complex Numbers
Some Basic Properties of Complex Numbers
This video describes some of the more basic properties of complex numbers.
From playlist Basics: Complex Analysis
ComplexMultiplication 1/3 - i/3
From playlist Complex Multiplication
What are complex numbers? | Essence of complex analysis #2
A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall
From playlist Essence of complex analysis
Complex Numbers - Division Part 1 | Don't Memorise
How can one complex number be divided by another? Watch this video to know more To access all videos related to Complex Numbers, enrol in our full course now: https://bit.ly/ComplexNumbersDM In this video, we will learn: 0:00 Introduction 0:15 Complex number divided by real number 0:46
From playlist Complex Numbers
Complex sine waves and interpreting Fourier coefficients
Now that you know the basic mechanics underlying the Fourier transform, it's time to learn about complex numbers, complex sine waves, and how to extract power and phase information from a complex dot product. Don't worry, it's actually not so complex! The video uses files you can download
From playlist OLD ANTS #2) The discrete-time Fourier transform
Solving Olympiad Level Geometry Problems with Complex Numbers #SoME2
Errata: At 9:20 the second -lambda should be replaced with +lambda At 13:09 we meant to say: "The astute scholars amongst you may have noticed that we just looked at Cartesian geometry up to this point." At 24:53 we meant to say: "We just know that D is somewhere on the line segment AC."
From playlist Summer of Math Exposition 2 videos
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 1) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Robyn Brooks and Celia Hacker (6/24/20): Morse-based fibering of the rank invariant
Title: Morse-based fibering of the rank invariant Abstract: Given the success of single-parameter persistence in data analysis and the fact that some systems warrant analysis across multiple parameters, it is highly desirable to develop data analysis pipelines based on multi-parameter per
From playlist AATRN 2020
This video lesson is part of a complete course on neuroscience time series analyses. The full course includes - over 47 hours of video instruction - lots and lots of MATLAB exercises and problem sets - access to a dedicated Q&A forum. You can find out more here: https://www.udemy.
From playlist NEW ANTS #2) Static spectral analysis
Claudia Landi (8/29/21): Discrete Morse Theory meets Multi-Parameter Persistence
Discrete Morse theory permits reducing a cell complex to the critical cells of a gradient vector field. Critical cells carry all the relevant homological information about the input data. Multiparameter persistence is a promising tool in topological data analysis of multivariate data that
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Nexus Trimester - Alexander Shen (LIRMM, Montpellier) 2/2
Different versions of Kolmogorov complexity and a priori probability: a gentle introduction Alexander Shen (LIRMM, Montpellier) February 01, 2016 Abstract: The informal idea – the complexity is the minimal number of bits needed to describe the object – has several different implementatio
From playlist Nexus Trimester - 2016 - Distributed Computation and Communication Theme
On Ultra-Parallel Complex Hyperbolic Triangle Groups by Anna Pratoussevitch
SURFACE GROUP REPRESENTATIONS AND GEOMETRIC STRUCTURES DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
Analytic Continuation and the Zeta Function
Where do complex functions come from? In this video we explore the idea of analytic continuation, a powerful technique which allows us to extend functions such as sin(x) from the real numbers into the complex plane. Using analytic continuation we can finally define the zeta function for co
From playlist Analytic Number Theory
Claudia Landi (5/11/22): Multi-parameter persistence from the viewpoint of discrete Morse theory
Although there is no doubt that multi-parameter persistent homology is a useful tool for the topological analysis of multivariate data, a complete understanding of these modules is still lacking. Issues such as computation, visualization, and interpretation of the output remain difficult t
From playlist Bridging Applied and Quantitative Topology 2022