# Welch Labs

• ### Imaginary Numbers Are Real [Part 1: Introduction]

2,758,800 views 3 years ago

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

Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook: http://www.welchlabs.com/re.... Show less

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• ### Self Driving Cars [S1E1: The ALV] - Duration: 8 minutes, 24 seconds.

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• ### How to Science [Part 6: Secret Math in Your Brain] - Duration: 7 minutes, 14 seconds.

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• ### How to Science [Part 5: Mathematics] - Duration: 12 minutes.

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• ### How To Science [Part 4: Science] - Duration: 8 minutes, 52 seconds.

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• ### How to Science [Part 3: Experiments] - Duration: 6 minutes, 30 seconds.

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• ### How to Science [Part 2: Our Universe = Math?] - Duration: 7 minutes, 23 seconds.

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• ### How to Science [Part 1: Music] - Duration: 3 minutes.

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• ### Channel Update [April 2017] - Duration: 6 minutes, 12 seconds.

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• ### Learning To See [Part 15: Information] - Duration: 13 minutes.

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• ### Learning To See [Part 14: Better Heuristics] - Duration: 12 minutes.

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• ### Learning To See [Part 13: Heuristics] - Duration: 9 minutes, 37 seconds.

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