I'm a computer scientist watching your videos who knows all of these concepts you are teaching, but I am still interested simply because you are an excellent teacher who seems to be passionate about the subject. Wish I had teachers like you.

His biggest flex is explaining complex things in 11 minutes

For anybody who cares, you actually find a lot of complex (imaginary) numbers in quantum mechanics. They do exist in nature, just maybe not as obvious as others.

Man.....,
I wish we had such teachers at our school,I would love going to school

Keep up the good virtuous hard work! You are an amazing teacher. You remind me, sadly, of just a couple I've had. Good teachers are few & far between. I'm so glad I stumbled upon your YouTube channel. thank you.

You are a gifted teacher.  I really enjoy watching your lessons. You are the math teacher that everyone should have had.

This video series is basically the history of maths

I love everything about complex numbers, like entire functions, contour integrals and independence of path.  It's as amazing and headache inducing as abstract algebra.

You're the best math teacher I've ever seen

I thought the most beautiful identity was Euler's identity since it shows a profound connection between the most fundamental numbers in mathematics. Euler's identity is often cited as an example of deep mathematical beauty. Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants 0, 1, i, e and π. It is the most beautiful mathematical identity known to man.
e^(iπ) + 1 = 0

10:22 Some would say Euler

Complex numbers are also used in Jolias/Mandelbrot formula, used to create colorful patterns in computer graphics.

Leged a legend!!  ~ ✨Such a great teacher 🌟💫✨

When I was a small child, my father (who had a math degree) had introduced me to negative numbers, and one day I came home from school upset, saying the teacher had LIED in math class: she said you couldn't subtract a larger number from a smaller one. I wasn't quite accustomed to (and of course she didn't mention) the fact that these sorts of statements are always relative to some domain of numbers: first- and second-grade arithmetic was operating in the natural-number domain, and I had already been given a peek beyond.

I am worried because I pay more attention to this than the students themselves

00:00 <---- Love at first sight 💘

The five dislikes was maybe by mistakes

Great explanation! I've always wondered what's the difference between imaginary and complex numbers. And also why it was chosen to be sqrt(-1) and not some other number

great video!

-1=e^i(pi)