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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

Want to learn more or teach this series? Check out the Imaginary Numbers are Real Workbook:

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Could you go a bit faster in these videos please, there were some parts I actually caught fleeting glimpses of

Every time I hear Euler's name pronounced it's jarring to me because I want to pronounce it as "yuler."

Hi, I'm math teacher. I find it much easier to tell my math equation to my students with Video Animation. Could you please recommend me the software you use for your animation?

Hang tight guys!

You're on the best playlist ever made..

You'll realize soon!

hit like if at your school, you were taught these were "complex" numbers.

https://www.youtube.com/watch?v=eGJpen6PpBU&t=269s

complex number..!

Remember mathematics is racist. Not only is Gause white, he was german, and all germans are nazis. As woke self hating white liberal, I demand these racist numbers be replaced seminars on inclusiveness and cultural sensitivity. Only after we get rid of the legacy of such racists as Leibnitz, Gause, and Newton and remake mathematics using the ideas of nonbinary non-white mathematicians can we end the systemic cultural racism that exist in the realm of numbers. Numbers are racist

euler: -1 > ∞

He predicted integer overflow

Euler…Kinda a big deal… he he

0 is from India

Algum Brasileiro para trocar uma ideia? Kk

How did you animate the graph? What is the quadratic equation in 3D?

The fact that we considered "imagination" isn't real so that leads to this type of numbers as well

so how about we accept one weird reality that imagination is real in some sense

COVID-19 ? Negative.

May be Invisible is a better name than Lateral.

India school predated the discovery

MUITO BOM!!!!

Blääääää😥⚀tuossa nyt nätisti mut käytänössä optiikka tieten muuttaa tuota lateraalia ja jne…

Best tutorial 🔥 you made these boring topics so fascinating, thank you so much

Anyone else here due to 3blue1brown's shout-out?

imma just gonna start making up mathematical concepts, seems to work. I'll invent a number Q that instantly solves any equation. QED

https://m.youtube.com/watch?feature=youtu.be&v=ING89_JacDk

lateral living in the time of gauss, ill ask him how he realise about those things, if it is a genius thing or is something that came from lateralation.

Everybody is a gangsta…

Till this guy says that imaginary numbers are real

Which software you are using for animations?

I love how this dude sounds like Pete Riley from Phantom of the megaplex.

LATER

oye y como se consigue la pendiente cero de esa funcion con los numeros laterales?

So does that mean my imaginary girlfriend is real?

Jk I don’t have one but I had to make this comment.

Thank you

I'm not saying lateral numbers don't exist, but at least all other numbers exist elsewhere in the universe. Whole numbers are obvious. Fractions are just parts of something, say pie. Some irrational numbers are naturally occurring, like pi, e, the squareroot of 2, etc. although I lack the words to describe it well.

And even negative numbers exist, with antimatter, which when added with normal matter, makes both disappear, just like when we would normally add -1 and 1 together. Thus also zero exists.

So there are really just 3 options:

1: Lateral numbers are imaginary.

2: We simply haven't discovered the real lateral numbers.

3: Lateral numbers are an exception to the rest of numbers (this is really just an excuse to not say it's imaginary)

wow man your explanaition is brilliant i saw it for the first time and understood it very well when its still from a grade a lot ahead of me thanks . and keep the good work up cuz your great in this

Anybody else despise Gauss just because of gauss's law lmao ?

"Imaginary numbers" is a fine term. The trouble lies with our disparaging colloquial usage of the word "imaginary." We often use it as a synonym for "fanciful" or "impossible," when, in reality, it is a perfectly respectable word.

3:51 "numbers are lame, let's invade something!"