3Blue1Brown
Visualizing quaternions (4d numbers) with stereographic projection
How to visualize quaternions, a 4d number system, in our 3d world
3Blue1Brown
Euler's formula with introductory group theory
Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.
3Blue1Brown
Visualizing quaternions (4d numbers) with stereographic projection - Part 1 of 2
How to visualize quaternions, a 4d number system, in our 3d world
3Blue1Brown
What are quaternions, and how do you visualize them? A story of four dimensions.
How to think about this 4d number system in our 3d space.
3Blue1Brown
Newton's Fractal (which Newton knew nothing about)
Newton's method, and the fractals the ensue
3Blue1Brown
Euler's formula with introductory group theory - Part 1 of 4
Euler's formula, e^{pi i} = -1, is one of the most famous expressions in math, but why on earth is this true? A few perspectives from the field of group theory can make this formula a bit more intuitive.
3Blue1Brown
e^(iπ) in 3.14 minutes, using dynamics | DE5
A quick explanation of e^(pi i) in terms of motion and differential equations
3Blue1Brown
Understanding e to the i pi: Differential Equations - Part 5 of 5
A quick explanation of e^(pi i) in terms of motion and differential equations
3Blue1Brown
Olympiad level counting: How many subsets of {1,…,2000} have a sum divisible by 5?
Timestamps 0:00 - Puzzle statement and motivation 4:31 - Simpler example 6:51 - The generating function 11:52 - Evaluation tricks 17:24 - Roots of unity 26:31 - Recap and final trick 30:13 - Takeaways
3Blue1Brown
Visualizing the Riemann zeta function and analytic continuation
What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
3Blue1Brown
Visualizing the Riemann hypothesis and analytic continuation
What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
3Blue1Brown
Where Newton meets Mandelbrot (Holomorphic dynamics)
How the right question about Newton's method results in a Mandelbrot set.
Curated Video
Complex Numbers
“Complex Numbers” will explain what a complex number is and how to apply operations to complex numbers.
Zach Star
Why imaginary numbers are needed to understand the radius of convergence
Why imaginary numbers are needed to understand the radius of convergence
Zach Star
The intuition and implications of the complex derivative
The intuition and implications of the complex derivative
Why U
Algebra 82 - Complex Functions
In previous lectures we have seen that quadratic equations that have no solutions when only real values are considered, do have solutions when complex numbers are allowed as input and output values. In this lecture, we check the complex...
Why U
Algebra 78 - Imaginary and Complex Numbers
The concept of imaginary and complex numbers was a powerful innovation that enabled mathematics to progress into previously uncharted territory. Although this concept was not entirely intuitive, extending our number system to include...
Brian McLogan
What is the complex number plane
In this video series I will show you how to graph complex numbers by graphing a complex number on the imaginary and real axis. We will graph these just like we graph coordinate points but now with imaginary axis.
Brian McLogan
What is the absolute of a complex number
In this video series I will show you how to find the absolute value of a complex number. The absolute value of a complex number represents the distance from a complex number to the origin. We will do this by taking the absolute value of...
Brian McLogan
Tutorial - Graphing complex numbers ex 4, 4
In this video playlist you will learn everything you need to know with complex and imaginary numbers 4
Why U
Algebra 80 - Multiplication with Complex Numbers
Multiplying a complex number by another complex number is accomplished using the distributive property to multiply the real and imaginary parts of the first number by the real and imaginary parts of the second number. In this lecture we...
Zach Star
The Mathematics of Symmetry
This video goes over the topic of group theory and gives a brief overview of how the mathematics of symmetry works.
Zach Star
How do complex numbers actually apply to control systems?
How do complex numbers actually apply to control systems?
Why U
Algebra 79 - Adding and Subtracting Complex Numbers
Addition and subtraction of complex numbers can be done arithmetically by adding or subtracting their real parts and separately adding or subtracting their imaginary parts. These operations of complex addition and subtraction can be...