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“Imaginary Numbers Are Real” by Welch Labs

Imaginary numbers are not some wild invention, they are the deep and natural result of extending our number system. Imaginary numbers are all about the discovery of numbers existing not in one dimension along the number line, but in full two dimensional space. Accepting this not only gives us more rich and complete mathematics, but also unlocks a ridiculous amount of very real, very tangible problems in science and engineering.

Part 1: Introduction

Part 2: A Little History

Part 3: Cardan’s Problem

Part 4: Bombelli’s Solution

Part 5: Numbers are Two Dimensional

Part 6: The Complex Plane

Part 7: Complex Multiplication

Part 8: Math Wizardry

Part 9: Closure

Part 10: Complex Functions

Part 11: Wandering in Four Dimensions

Part 12: Riemann’s Solution

Part 13: Riemann Surfaces

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