What is a phase plot? - Complex Analysis

[@LuffinaCHuang]

Enjoy your video every time. One of the best math courses I ever had.

[@kisonecat]

That is very kind of you to say! Thank you!

[@black_jack_meghav]

Hi prof! Will there be full course on complex analysis? Like mooculus?

[@Poetria1]

I would gladly take it. :)

[@kisonecat]

I probably can't do a full course right now, but I am going to make more videos (at least on a weekly schedule). If there are particular things you'd like to see, please let me know!

[@black_jack_meghav]

@@kisonecat okay sir , we understand. I would appreciate any videos you make. Thanks!

[@punditgi]

@@kisonecat Whatever you can upload. Incremental steps, monsieur!

[@aBigBadWolf]

Hey, here from one of your other videos. Question: why do we put the even grid and regular colors in the codomain and not in the domain? Now the plot of the domain at 5:18 is showing the inverse of cos z, no? Cool stuff though!

[@kisonecat]

That's a great question. The coloring is such that each point in the domain is colored to reflect its destination, so the codomain gets the boring plain grid which then is pulled back to color the domain in an interesting way. Something similar happens with a graphic like commons.wikimedia.org/wiki/File:US_population_map.png where the 'domain' is counties, and the codomain is a number line, colored with bigger numbers being red and smaller numbers being green. The counties are sent to their population on that number line, and the color is 'pulled back' from that number line to paint the county. It can really feel like this is backwards, and the fact that both the domain and codomain of a complex analytic function are BOTH the complex plane makes this more confusing.

[@ghinahmaidosh5457]

Wow wow wow wow wow wow wow