Imaginary Numbers Are Real [Part 1: Introduction]

The greatest audiovisual content on the topic I have ever seen: Part 1 - [VIDEO] Part 2 - [LINK] Part 3 - [LINK] Part 4 - [LINK] Part 5 - [LINK] Part 6 - [LINK] Part 7 - [LINK] Part 8 - [LINK] Part 9 - [LINK] Part 10 - [LINK] Part 11 - [LINK] Part 12 - [LINK] Part 13 - [LINK]

Welch Labs has a wonderful series on youtube on imaginary numbers, "Imaginary Numbers Are Real": [VIDEO] I like to tell my kids that imaginary numbers aren't really imaginary .. that in many ways they're more real than the Reals.

I really enjoyed this video series on imaginary numbers. Went through the history as well as the math: [VIDEO]

I agree that for most of advanced math, VR won't help, however there are a lot of mathematical concepts that are easier to grasp when visualized. [LINK] [VIDEO] [LINK]

For a small buffet of abstract math topics (with lots of exposition putting ideas into historical context and an emphasis on building geometric intuition) try Courant & Robbins "What is Mathematics?". Covers number theory, number systems, geometry, topology, optimization, algebra, and knots, among others. You could also play around with branches of math like Knot and Braid Theory, which are interesting in their own right, give insight into lots of different branches of math, and many interesting problems are still accessible to lay people. Number theory is also like this I think it can also be helpful to learn some things about the history of math and the historical context that different ideas came from. Here's a nice example covering complex numbers [VIDEO] Maybe tangential to your ends, but the Crest of the Peacock is a nice book on non-European mathematical traditions, which provides some insight into how the process of establishing and validating mathematical knowledge works in other cultures. You might try books written by physicists or that are about mathematical physics (an author to look out for depending on your level is VI Arnold), since arguments will be of a more geometric or physical nature and appeal more to intuition. Stillwell is another author (not a physicist) that tends to write books that give context and geometric intuition You might like playing around with Pinter & Humphreys for Algebra, or Jänich for Topology (fantastic book for building intuition aro

Welch labs has an amazing series on complex numbers called “imaginary numbers are real”. Great explanations, engaging content and high production value. [VIDEO]

Yes, the name imaginary does it no favours. I was confused for so long about i, as it was never explained on classes, and it wasn't until 3blue1brown and other math youtubers showed me the light. I really like this series on it by Welch Labs - loads of easily digestible videos, and a history lesson to boot: [VIDEO]

Regarding imaginary numbers, I found this YouTube series really helpful to understand basics of imaginary numbers. [VIDEO]

I really like the welch labs series on imaginary numbers which covers the first part of what you talk about -- leveling up the notion of what a complex number is. Though his focus was more on solving simple equations with no real roots, but really detailing how/what is really going on. It is a great precursor to then thinking about quaternions [VIDEO]