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.
Overview
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
