Visualizing simple complex functions -- Complex Analysis 3

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[synaestheziac]

31:20: “the burger in the world where 5 exists” - without context, this message is delightfully absurd

[jorgedaniel]

Thanks for every single video. I just recently found out you had this channel and can’t wait to see them all.

[kaasci]

For somebody not familiar with complex analysis, is there any kind of companion book you'd recommend for following these? I've been using Axler alongside your series on abstract linear algebra

[vancenannini]

Really nicely done. I also love the chalkboard work. I tell my students that nothing sound likes learning better than a piece of chalk on a chalkboard - markers DON'T do it 😊

[TheOldeCrowe]

At 28:27 the equation should be v = ½(u²–1) instead of v = ½u²–1

[romajimamulo]

16:43 I hope you meant negative real axis
EDIT: You keep calling it that, and I'm not sure what you should do to fix it

[aweebthatlovesmath]

Finally i understand this topic thank you so much this helped a lot

[aniruddhvasishta]

At 14:06, if you interpret the argument as -pi/2, the new argument is -pi/4 which is what you drew, but if you interpret it as 3pi/2, then the new argument is 3pi/4, which is what you drew for the other function. How do you know which is which?

[andersok]

14:00 If you think -i as e^i(3/4)pi instead of that negative argument you end up with a different point. What is going on?

[sunev]

Great video. But the font size in the mathematica is too small. I think the demostration will be much better if you enlarge the font by "magnification" in the "window" menu.

[georgelaing]

In the last expression for v there should be parenthises around u squared minus 1.

[half_pixel]

I'm a bit confused about the parabola at 28:42. i is a point on the line y=x+1, but i^2 = -1, and -1 is not on the parabola v = u^2-1. How could that parabola be the image in that case?

[vizart]

Isnt the reason you have to do a branch cut is if you didnt theres no way to make your squareroot functions continous? To make them singular valued really isnt a problem.

[atreidesson]

"The burger in the world where 5 exists" is what

[alfykerolous]

is there a text book or a reference i can stufy complex analysis with this course

[milenamarquez]

Please somebody tell me how to solve for x^2+(y-1)^2 = 4 under w = z^2... it is not going to be a cardioid, and I am stuck.

[Toni-chzx]

14:02 confuses me. Couldn't you say that the argument of -i is 3π/2, mapping in to the second quadrant? Equivalently, using the negative root, -i would end up in the fourth quadrant.

[Alex_Deam]

I'm confused by the Riemann sphere. Looks like if you match the pluses to the pluses etc then you end up gluing the 0 from the top half to the infinity from the bottom half (and vice versa). Also, I don't see how this solves the problem of it not being a function - isn't every point in the complex plane mapped to two different points on the sphere still?

[sinecurve]

Will this series cover topics like "the method of steepest descent?"

[mals]

Can someone explain what is being said at 9.30 about everything above the x- axis getting mapped to the entire plane? I don't understand that part
thanks