Imaginary Numbers, Functions of Complex Variables: 3D animations.

Visualization explaining imaginary numbers and functions of complex variables. Includes exponentials (Euler’s Formula) and the sine and cosine of complex numbers.

[EugeneKhutoryansky]

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[ultravidz]

You do a great service to mankind with these videos.

[FPrimeHD]

I feel like I won the lotto finding this channel. I'm taking complex analysis and it's nice seeing what this looks like. I'm struggling to get my brain wrapped around the principle branch lol.

[Guelop]

I've never imagined this kind of animations were possible, and what's more, they just show the beauty of physics, maths...

Just wow... 10 out of 10. Brilliant job done here.

[davem]

I really hope we look back on these videos in 50 years as the start of an educational revolution. Education all the way from K-12 to university is nothing but a cash cow for adults that don't give a damn about their students. Free access, repeatable, archived, and in an ideal world you get paid more the better job you do. Contrast that to even small non-doctoral schools whose admins are pushing teachers to get NSF/DOD grants because they get to suck up half of the award. Somehow they have to do that and teach 4.5 classes a semester. The students aren't the ones winning in that system

[EugeneKhutoryansky]

I recently created a Patreon account for people who want to help support my channel. The link is on my YouTube home page. Also, in case, you have not already seen them, I uploaded several other videos recently. As always, for each video that you like, you can help more people find it in their YouTube search engine by clicking the like button, and writing a comment. Lots more videos are coming very soon. Thanks.

[DayaCIDfan]

I absolutely adore the work that you are doing. It is helping me soooo much thaat I will probably donate my first salary to your channel. These videos, if taught by a professor would cost in order of hundreds of dollar per class but here, it is free. I promise to make a humble donation next month when I get some money. I have already put that on my calendar. Thank you extremely very much for your videos, I hope you find everything that you are looking for from life!

[kjreich]

what's with the music???? i feel like I'm at a medieval festival or in a video game.

[SOBIESKI_freedom]

BEAUTIFUL!! You, sir, are a genius and a prodigy! Keep 'em coming! I can't get enough of these intellectually intoxicating grand opuses.

[altuber_athlete]

6:25 Usuallly, the length of a complex number is called the _magnitude_ of it (as you said), however its angle is called the _argument_ of it. When dealing with signals (as in AC circuits), the magnitude is then usually called as the _amplitude_ of the signal, and the angle is then called the _phase_ of the signal.

This is not a mistake you made ;) I'm just saying this so people can have a better vocabulary.

As always, these videos are extremely awesome!!!

[yashmehan]

who are these 29 sinners who dared to dislike your video??? they mus be punished.
Great btw, later half of the video flew above my head, but i encountered somebody for the first time who could make me understand this topic in this much detail.

[huciiyh]

these videos make me scared
the music, the animation, the voice, the subject!

[diasmashikov]

I do not know how many people worked on this, but I am so much grateful for making such videos. They help and impact a lot. Thank you very I hope your work gets the necessary awards in real life.

[meandyousomeofusfortwo]

I finally understand why i^2 = -1. Thank you

[floodingthesea]

When a professor cannot be understood, find relevant YouTube videos you should.

And oh boy... I stuck gold. This video is the best video I've seen on the subject.
Very good for visual learners. Very well made.

This is the most honest and deserved sub I gave anyone.

Thank you

[leecoates]

This channel is a life saver! I'm very much a visual type learner and benefit massively from the videos this channel provides, great for Electrical Engineering students - Thanks a lot!

[tonyrosam]

Math is my religion and knowledge is my weapon. I am truly honored to
live long enough to understand this. Bless all of you who feel the same.
The light is spreading slowly but at least its spreading. Now if we
could stop the money pigs from destroying Earth in my lifetime that
would be awesome! Join me and lets change the system from the inside out!

[ahappyimago]

I love you. Because of you I studied math and physics and intuitively understand better than I would have ever done from school.

[EugeneKhutoryansky]

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[destinpearson]

What I love about your videos Eugene is that instead of just learning a concept, I actually understand it and how it works, it is actually quite interesting once you understand a concept for its entirety. Thank you