Summer of Math Exposition

I liked the music, the animations, everything really. In my opinion, nothing could really be improved, this would make for a great video to show as an introduction to complex analysis in a class.

Great visuals, explanation could be 0.9x speed, good pacing and clear progression and plot.

A bit dry or textbookish, a good illustration of basic facts of complex multiplication for someone who already knows it; a bit abstract for those who don’t.

If this was your first video, amazing quality! Maybe next pick a more niche subject that lights you up personally. Going for broad mass appeal (who wouldn’t need to understand complex multiplication? True, but it) almost necessarily makes for less exciting videos.

Complex number operations is a standard textbook topic, and I think you covered the basics quite clearly and at a good pace. Reason why I didn’t score it higher is also because it’s a standard topic. It’s already covered by a lot of books and curriculums. Everything was as I expected so it didn’t have the novelty factor.

The explained the intuuition with clarity and enthusiasm.

Really nicely paced video. I could tell you had a plan and a story you wanted to tell, but you took your time in your explanations so your viewer had time to really digest what you were showing them. I agree with the motivation at the beginning, to paraphrase “there is a fundamental difference between looking at the equation of a circle and seeing the attributes of a circle on a graph.” I’m a data analyst, and there is a rule of thumb that the first step of data analysis is just looking at the data without any manipulation. You’ve done a great job of slowly building up your case, and I think you chose a good path to bring your student to a point where they could start to understand graphic understandings of imaginary numbers. I don’t use them frequently in my own work, so this has given me some nice takeaways too. I’m not quite sure how novel this particular analysis is, but your particular approach and structure to the lesson was good enough that I wouldn’t mind sharing it with someone who wants a better insight into what imaginary numbers “are”.

Thank you for this great submission!!

There was a lot I liked:

• The introduction is sure to get people interested, especially the rhetorical questions. I agree with your point, learning maths from a visual angle can be very beneficial!
• Your video is well suited for students who have perhaps learned a little bit about complex numbers already, but are ready to see it from another perspective. As a result, I felt it didn’t include TOO much background on complex numbers, but also wasn’t rushed, great job.
• It is very effective how you start by showing a concept in the real numbers before you extend it to complex numbers. This helps students extend their knowledge whilst feeling confident!
• The visuals in the multiplying by a complex number segment were extremely well done.

Here is what could have made it just slightly better for me:

• Relax the pace a bit more. This can help with clarity. For example, after you ask a question like “What happens when we multiply by negative numbers?” take a pause to let the viewer ponder!
• The last example of the multiplication could have taken more of a step-by-step approach with intermediate goals so students can follow along the way.
• I wasn’t sure the angle was exactly unique or novel. I think a lot of students do already learn about the geometry with complex numbers. But it is helpful none the less.

Great job, and thanks for making it.

Great explanation for a standard topic. I think it would have been nice to show more in depth properties of complex numbers in geometry like conjugates, perpendiculars, etc.

Phenomenal video! I love how simple you made the idea that multiplying by i rotates a number 90 degrees. The way that you put it, where you mentioned that multiplying by -1 rotates a number 180 degrees and i just does half of that makes so much sense. I also think it was a great idea to show the application of that to then the larger problem of multiplying 2 complex numbers. I think the explanation for why the magnitude of the product is the product of the two magnitudes was maybe breezed through too quick or maybe a step too far for this video, but I do like that you are hinting at a larger world to explore out there though. Overall however, animation was good, the narration flowed very nicely, it was a very solid and easy to follow video! I think a student versed in algebra but maybe not imaginary numbers could easily get the hang of the basics with this.