Necessity of complex numbers

7:00 (When very good physicist are wrong, they are not wrong for silly reasons, but they are wrong for good reasons, and we can learn from their thinking.) I love it!

See you all next year when the algorithm brings us back

gauss hated the name imaginary, because it's confusing.He suggested to use lateral, because the complex number are represented on the lateral axis unlike all other numbers.

I am not mathematics major. But whenever I watched videos regarding math it brings Peace in heart. I don't know why

Barton Zwiebach is peruvian. He was born and studied school and electical engineering in Lima, Peru. As a peruvian I feel so proud of him.

I had to learn this by distance education (1992) before the internet and always struggled. Barton makes it seem so easy. What a fabulous lecturer.

I clicked because I thought he was a young Harrison Ford. Now I know how complex numbers are crucial part of wavefunctions in quantum.

If I ever strike it rich, I would love to go to MIT to study physics at leisure with amazing teachers like this...

What a great introductory video. The professor is comfortably understandable and thorough.. Fantastic, short introduction to complex numbers and their importance. Thanks for posting!.

As a peruvian I feel proud of Barton, he is the best student of the National Engineering University in Lima Peru

I am a teacher at the beginning of my career. That was a very inspiring explanation.

Men of curiosity ,we meet again

Fantastic, short introduction to complex numbers and their importance. Thanks for posting!

Honestly, this was probably the best introduction to quantum mechanics i'ver ever heared. Before you get to this whole superposition shit and stuff, first explaining the fundamental maths behind it, which by all means isnt that hard to not teach it to students. Great job.

Very nice short note on complex numbers. A great professor tells you much more than just writing down those dry equations.

Great video. I’m reading Ruel Churchill’s book on complex numbers and applications. I like his introduction. Instead of starting with the definition of i as the square root of negative one, i is introduced as part of a function that is necessary for certain equations (an ordered pair with certain, somewhat unusual mathematical properties). As, I read it, the fact that it turns out to be the square root of negative one is more a consequence of the definition , rather than the basic definition of i. It’s a subtle point, but that explanation sits better with me. Most modern books start with “i is the square root of negative one,” and that’s harder to get my head around than the more fundamental definition.

When I studied this subject 25 years ago, back on the engineering classes, I remember I got to understand the topic quite well as it was necessary to solve circuits problems. But I never got to use that on the real world, and now it is a "complex" concept for me. Anyway, I hope someday I have the time to brush up on my advanced maths.

I thought that was Harrison Ford in disguise

This brings me back to the good old days of engineering school. Ironically I miss it. I felt so sharp in my mathematical skills.

Very pure very clear very quality lecture series on QM and QFT...!❤💜❤