# Welch Labs

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

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https://www.patreon.com/wel...

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

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

• ### Self-Driving Cars [S1E4: RALPH] - Duration: 12 minutes.

• 21,521 views
• 6 months ago
• ### Self-Driving Cars [S1E3: AI Failure?] - Duration: 10 minutes.

• 18,897 views
• 6 months ago
• ### Self Driving Cars [S1E2: ALVINN] - Duration: 11 minutes.

• 23,866 views
• 7 months ago
• ### Self Driving Cars [S1E1: The ALV] - Duration: 8 minutes, 24 seconds.

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

• 23,252 views
• 1 year ago
• ### How to Science [Part 5: Mathematics] - Duration: 12 minutes.

• 23,812 views
• 1 year ago
• ### How To Science [Part 4: Science] - Duration: 8 minutes, 52 seconds.

• 20,691 views
• 1 year ago
• ### How to Science [Part 3: Experiments] - Duration: 6 minutes, 30 seconds.

• 23,004 views
• 1 year ago
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• ### How to Science [Part 2: Our Universe = Math?] - Duration: 7 minutes, 23 seconds.

• 39,736 views
• 1 year ago
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• ### How to Science [Part 1: Music] - Duration: 3 minutes.

• 44,398 views
• 1 year ago
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• ### Channel Update [April 2017] - Duration: 6 minutes, 12 seconds.

• 25,347 views
• 2 years ago
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• ### Learning To See [Part 15: Information] - Duration: 13 minutes.

• 30,338 views
• 2 years ago
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