Complex Numbers and Functions in Algebra and Geometry

JMM 2025: AMS Special Session on Take the i Road: Welcoming Complex Numbers and Viewpoints Across the Undergraduate Curriculum Complex Numbers and Functions in Algebra and Geometry https://flashman.tiny.us/JMM2025 Dedicated to the memory of Ruth Favro [1938-2023] and David Orme Tall (1941-2024) Though the complex numbers play an important role in analysis, I will present a visualization of complex numbers and functions with mapping diagrams (using GeoGebra) that helps illuminate the study of algebra and geometry. In particular, in algebra the focus will be on visualizing roots of complex polynomials. In geometry the focus will be on visualization of isometries, dilations, and inversions with complex functions/maps. Questions may be emailed to me at mailto: flashman@humboldt.edu

Complex Numbers and Functions in Algebra and Geometry

Table of Contents

Introduction

Mapping Diagrams: Visualizing Real and Complex Functions

Complex Numbers in ALGEBRA: Understanding and Solving Quadratic Equations

Visualizing Complex Arithmetic

Complex Numbers in Geometric Transformations: Isometries, Dilations, Inversions

Thanks and References

New Resources

Discover Resources

Discover Topics