YoVDO

Complex Number Fundamentals - Lockdown Live Math

Offered By: 3Blue1Brown via YouTube

Tags

Mathematics Courses Geometry Courses Complex Numbers Courses Imaginary Numbers Courses

Course Description

Overview

Dive into the geometry of complex numbers in this comprehensive 1.5-hour video lecture. Explore fundamental concepts, including rotating coordinates, multiplication properties, and angle addition. Learn through interactive demonstrations using GeoGebra, Python, and Desmos. Tackle challenging questions, discover practical applications like image rotation, and gain insights into the relationship between complex numbers, vectors, and matrices. Master the "cis" shorthand and connect various mathematical concepts in this engaging exploration of complex number fundamentals.

Syllabus

- W3 Results.
- W4 Prompt.
- Ask What would you call 'imaginary numbers'?.
- Startingpoint & assumptions.
- W4 Results.
- Q1 Prompt.
- Q1 Process.
- RotatingCoordinates.
- Q1 Result.
- Q2.
- Q3 Prompt.
- Q3 Results.
- RotationAnimation.
- 3 facts about Multiplication.
- Q4 Prompt.
- Ask imaginary I vs physics i&j.
- Q4 Result.
- GeoGebraDemo.
- Q5 Prompt.
- Q5 Results.
- Q5 Solution.
- RotatingImages Example.
- PythonExample.
- PythonImage Rotation Example.
- Ask Vectors & Matrices for rotation.
- Q6 Prompt.
- Q6 Results.
- Q6 Solution.
- RedefiningAngle Addition.
- Q7 Prompt.
- Ask Can we do without complex numbers?.
- Q7 Results.
- Q7 Solution.
- Q8 Prompt.
- Ask sum/difference of angles.
- Q8 Results.
- Q8 Solution.
- DesmosExample.
- Bringing it all together.
- The "cis" shorthand explained.
- Q9 Prompt.
- Q9 Results.
- ClosingRemarks.


Taught by

3Blue1Brown

Related Courses

Imaginary Numbers Are Real
YouTube
Trig & PreCalculus Vol 1
YouTube
Algebra 1 - Unit 11
YouTube
Algebra 2 Course - Unit 8
YouTube
Algebra 2 Course - Unit 9
YouTube