How to Construct the True Complex Numbers I - Famous Math Problems

Explore the construction of true complex numbers in this mathematics lecture. Delve into field theory, finite fields, and linear algebra to understand how complex numbers can be constructed over any field. Learn about three beautiful candidates for complex numbers associated with Euclidean and relativistic geometries. Discover innovative approaches to expressing negative numbers and gain insights into strengthening the concept of complex numbers for the 21st century. Examine the limitations of traditional complex number representations and explore a more rigorous mathematical foundation using 2x2 matrices over general fields.

Introduction
History of complex numbers
Field theory
Finite fields
Commutative laws
The path forward
Linear algebra
Diagonal matrices