Imaginary Numbers Are Real [Part 8: Math Wizardry]

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

[ABCDEF-vdwg]

Wow. Thousands of years of mind-blowing work spoon-fed to me in 30 minutes. I don't deserve this.

[CdeHwler]

This is... just... so beautiful. You rekindled my love for mathematics. Thanks you.

[lorenzomatteo]

Now WHY did they not teach me all this extremely BEAUTIFUL AND USEFUL stuff in college?

[ankush]

brilliant. i have watched all the parts and its brilliant

[dracos]

This is the point at which you blew my mind. This is the sort of explanation that would have come in handy during school.

[Greg]

I'm loving this whole series! I have a 6 year old and a 2 year old currently. I've been thinking for a while now about how best to tutor them at home for their math. I remember growing up and and really having to struggle outside class to make up for what I didn't understand during the lecture. My dad was an English professor, so he didn't really have a huge grasp of more complicated subjects that he had studies decades previous. My education in Medicine helps a bit, but still, just because you know something, doesn't mean you can teach it effectively. The complex numbers are a hugely important concept and one that, I think, is taught very poorly at the primary school level. Your series is extremely concise and eminently followable (is that even a word?) Thank you very, very much for this presentation!

[cooltv]

as someone who is naturally good at math and has almost never been surprised...

...my mind got blown when you put the unit circle over the grid
im going to apply this sorcery to things like 2^3, or x^3+2x^2+17x+8 for a while, and im going to enjoy it
ive not had a rabbit hole like this since 4th dimensional space! im excited!

[AbhishekVaid]

I am 31 years old and I'm a graduate and post-graduate in computer science. But this is the first time and it is today, that I'm learning and "understanding" math. Amazing stuff. Mindblowing!

[AlexeiRamotar]

Seeing this so late in life. Wish I had a repeat. Beautiful explanation.

[ayushchoubey]

Teachers like you that explain such concepts with ease are also no less than wizards in my eyes

[goopypuff]

These videos are amazingly clear and have super high production quality! Good work +Welch Labs !!!

[jivejunior]

0:51 "No, it's not that kind of video" XD

[jnaneshvb]

This is the best representation of "Cube Root of Unity" I have come across!
Thanks Welch Labs.

[VIRAJBHOSLE]

It's hard to explain in REAL words how amazing it was to discover all this about 'i' !! Thanks a lot!

[polarisgemini]

One thing I am learning from this video essay series is how crucial it is to teach maths using the number line. It's not only useful, it's easier to teach because the visualisation helps and actually shows us how the world is made up of numbers.

[grzegorzwasaznik]

"Now, are there more numbers?" *Vsauce music starts playing*

[ilanrodriguez]

I love imaginary numbers and complex derivatives. However I really want to do one ultimate thing. Is it possible to have a graph that shows all 3 major axis ( length width height ) while ALSO including the complex plane? I anticipate that it will clear up and provide closure to the concept of "imaginary" numbers.

[In-N-Out]

This is entertainment in its purest form.

[billmccaffrey]

I learned about "imaginary" numbers in 1970 high school math and as an engineer, used them often. This is the most intuitive description that I have seen. Wish I would have seen this in 1970.

[shafey]

Oh my god! That's how De Moivre's Theorem for finding complex roots works!
I'm speechless! This is mind-blowingly beautiful!