Imaginary Numbers Are Real [Part 1: Introduction]

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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

[masterstealth]

“We’ll be using the term lateral from now on”

*continues to say imaginary*

[aTomallic]

I remember a time where I was joking around with my algebra 1B teacher;
"Hey it's kind of wacky that the calculator responds no real numbers does that imply the existence of imaginary numbers?"
"Yes."
I cannot describe the internal panic I had at the idea of seemingly non-existent numbers.

[brlliantplanets]

By the way, imaginary numbers ARE called “lateral numbers” in China.

It could just because it’s easier to pronounce(less syllables in the Chinese language), but Gauss would be proud

[eziola]

Man, this is one of the greatest, mind-opening playlists about the beauty of math that has ever been posted to YouTube. This taught me to see algebra visually. Absolutely incredible. You are so talented. Why did you stop making series like these? They're incredible!

[SuperPBrady]

I’m a tutor and every time I explain imaginary numbers to precalculus students they are so confused. Your graphic here illustrates it perfectly. Thank you for taking the time to do this!

[billcannon]

You delighted me with the 3D lateral-plane visualization. Well done.

[maxwellscheinfield]

I show this first video of the series every single semester that I teach Algebra students about "imaginary" numbers for the first time. Really gets through to them!

[nuklearboysymbiote]

euler: -1 > ∞

He predicted integer overflow

[kswiorek]

In polish it's even worse. Imaginary numbers are "liczby urojone", "uroić" means to hallucinate...

[Black_Kakari]

Brah, he pulled a rainbow out of his paper.

Drugs

[TJShare]

Thank you so much! Your 3d animation was apparently what I needed for the imaginary numbers to finally make sense. It's a great feeling discovering the missing piece you need to understand a concept.

[DrPG]

The easiest way to understand real and imaginary numbers is by using my bank account balance as an example: its real part is $10 and its imaginary part is $10 million dollars.

[rinfeast]

its all fun and games in math class until the graph starts speaking 3d

[august_klevberg]

The easiest way to understand negative numbers is by picturing my bank account.. 😔

[nehalkalita]

Your efforts for making a whole playlist on imaginary numbers is worth of appreciation. Very few can explain in details.

[JabrHawr]

i'm loving this. gotta bookmark this and watch the rest of the parts.
the talk about the negatives being 'unnatural and weird' is extremely relatable - not now of course, but back when i was in school when i was first introduced to it.
and then you use this very relatable notion to explain how 'imaginary' numbers are exactly the same in that they may _feel_ unnatural but in truth they aren't (just like how we initially felt about negatives) - that is so good and appreciated. very exciting.

[jalfire]

thank you Gauss. It sounds much less awkward to say that I have a lateral girlfriend

[mab]

2:50 I know many of you just wanted to see this

[mathmagic]

Hey, this is really cool. I love the animation for "lateral numbers". I have started seeing some of the impact of imaginary numbers watching 3b1b's series, but he just sort of travels around a unit circle with them. Lets see how the next videos in the series do.

[papaluskask]

Maths works really well in network analysers. In high frequency work, telecommunications industry etc. You have to work in 3 axis, frequency and time but also voltage