History and Uses of Complex Numbers (UMAP)

This unit presents the history, the algebra, the geometry, and a few uses of complex numbers, including complex square roots and complex quadratic equations. It then explains the algebraic solutions of cubic and quartic equations. Finally, it is demonstrated how complex numbers arise in geodesy.

Table of Contents:

INTRODUCTION

THE HISTORY OF COMPLEX NUMBERS

THE ALGEBRA OF COMPLEX NUMBERS

THE GEOMETRY OF COMPLEX NUMBERS
Lengths
Angles
Roots
Dot Products, Determinants, and Applications

COMPLEX SQUARE ROOTS AND QUADRATIC EQUATIONS
Factoring and Solving Real Quadractics
Complex Square Roots by Algebra
Complex Quadratic Equations

EQUATIONS SOLVABLE BY RADICALS
Complex Cubic Equations
Trigonometric Solutions of Real Cubic Equations
Complex Quartic Equations

QUARTIC EQUATIONS IN GEODESY

SOLUTIONS TO ODD-NUMBERED EXERCISES

REFERENCES

ABOUT THE AUTHOR