Imaginary Numbers Are Real [Part 5: Numbers are Two Dimensional]

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

[rynabuns]

That rotating by 90° thing blew my freaking mind!

[morzee]

Oh my I'm training to be a maths teacher and at no point during my school education or my university degree did anyone use geometry to explain why you need imaginary numbers. It makes perfect sense! No doubt I'm going to be using that technique to teach my students for years to come so hopefully they understand it way faster than I did! Thank you so much :D

[Favourites]

you have no idea how much you helped me.

[drewgieman]

Can't believe complex numbers aren't taught this way in school. This is amazing.

[zestoslife]

OMG - I did a degree in Physics, and most grad work in opto-eletronics were "i" was used and know 20 years later I finally feel I understand i for the first time. Wow, amazing, lost for words. You'll are amazing.

[nju]

I wish my high school maths teacher was as good as you. I'm a engineering grad student and use complex number all the time. Know the formulas and equations but I always think of imaginary numbers as a hack for computing. After watching this its becoming more meaningful to me. Thank you

[awseomgyhero]

so is there any end to the mind blowness of maths?

[marco.nascimento]

This series is just amazing. Never understood how imaginary numbers are perpendicular to real numbers, and you just explained it so easily. Keep going with the awesome work!!

[alexanderhess]

I wish I could megalike videos. This is amazing.

[NickTheHunter]

I literally cried at the end of the video as I got emotional over how beautiful the explanation is and how useful they really are

[chuffmunky]

Thankyou! Why couldn't my £40 textbook just explain it as rotating through a second dimension?! Bloody waste of trees lol.

[mikeunleashed]

my understanding of imaginary numbers have increased so much from this XD thank you

[coltonHD]

I don't have any math that says so, although I feel like it should exist by now, but if numbers are two dimensional, could they be three?

[obits]

As a visual learner, this video series has done more to explain imaginary numbers than any of my AP classes ever did.

[dbajpeyi]

I am trying to learn audio signal processing and wanted to revisit some algebra and complex numbers. Bumped into this video, and realised how easy they can be if studied in the correct way. This video is just genius how it's explained. It's like now I will never forget what complex numbers anymore :D

[praisethesun]

Wow I never though about negative multiplication like that 2:20

[roozbeh]

only 700 views? shame on your people, this guy is the only person who describes imaginary numbers in an understandable way, that was a question which baffled my mind for years and I got the answer here

[think_in_a_blink]

Can't believe how interesting this simple problem can get... Literally getting more and more excited after watching each part....

[ABCDEF-vdwg]

Everything ties in beautifully now. I have honestly learned more in 15 minutes than an entire year's worth on the subject in school could have offered. Thank you!

[swerloop]

i wish i had seen this video twenty five years ago, when i was in school and struggling with these concepts. thank you.