What are Branch cuts,Branch Points and Riemann Surfaces(complex analysis part-10) by mathOgenius.

[@shegeley]

And this, ladies and gentlemen, one more topic when nor reading my professor's notes neither reading MIT tutorial helped me but the random smart Indian guy on KZbin did! Applause

[@mathOgenius]

One of the best Comments I ever got! Thank you these appreciations works like fuel , Really happy to Help!

[@samayaparibartan883]

Indeed

[@pasindubandara8358]

I even watched the lecture again. But still, I had to come here.

[@zacharyalonzo6164]

i guess Im randomly asking but does anyone know of a way to log back into an Instagram account..? I stupidly lost my login password. I would appreciate any tricks you can give me!

[@mathOgenius]

I hope the video helps! Please share!

[@Explore_With_Sagar]

It really helped. Please suggest a book to study these things.

[@Srinivasan15331]

Yes bro your videos are always helping us

[@srishtiagrawal1217]

Thank you so much i thought i would die learning reimann analysis but this video saved me its not the difficulty of topic its the ease of explanation

[@mathOgenius]

Glad it helped!! please share to support !

[@standup4you]

You are literally a genius

[@mathOgenius]

thanks .. ! please share to support!

[@karankakkar3999]

Good, clear and concise explanation. Well done.

[@mathOgenius]

thank you ! please share the video to support this channel .

[@dixitkumar9050]

You damn genius in maths..... thanks for such difficult topic explained in layman's terms

[@mathOgenius]

Thanks for appreciating! Please share the video to support my channel :)

[@larsybarz]

Brilliant. Thanks a million times

[@mathOgenius]

your welcome!! please share to support:)

[@lemyul]

thanks self proclaimed genius /s

[@mathOgenius]

🤣🤣 no no.. this is just the channels name :)

[@alikiaee1307]

Thank you for the video. I think there might be a small mistake at 11:03. In the case of two poles at +/-i. if we consider the argument range of the whole (Z^2+1) to be 0 - 2pi then, as you mentioned, the portion of the imag axis between the poles is included in the branch line. because on the line Z^2+1 becomes a positive real number. for the same reason, the entire real axis also becomes a branch line. you can check that by plotting the real value of the function in Matlab which shows a clear discontinuity at the real axis (make sure you restrict the argument to 0-2*pi). is there a point I am missing?

[@Ricky-Noll]

super helpful thank you

[@mathOgenius]

happy to help !, please shate the playlist to support

[@sayanjitb]

in the first example, if I take a rotation (theta + Pi) around the origin , then also its value changing by the factor "i".Please explain it.

[@mathOgenius]

Yes .. you are right we are getting a differnet value but .. it's a different point on the graph and we can get differnet values there.. but the problem is the different value at same point..

[@sayanjitb]

​@@mathOgenius Thanks a lot!

[@Explore_With_Sagar]

Thank you so much bro. Can you suggest me a book to study these things in details ?

[@mathOgenius]

I studied complex analysis In the book schaum's outlines complex analysis,and mathematical methods of physics by arfken.

[@riseldakodra4958]

how do you understand that the value of the function changes when you make a rotation? how do you prove it changes? especially when the branch point isnt the origin?

[@mathOgenius]

the center changes like If there is z then center is 0 and if like z-a then center is a

[@riseldakodra4958]

@@mathOgenius yes, i understand this part but i dont understand how to prove that the value of the function will change during the rotation ...how to prove that the value will pass to the next riemann surface

[@mathOgenius]

put that in the function .. the period and the value will change

[@khushbu5787]

Why we use branches in logarithmic functions ? Is it may be applicable in real number system?

[@mathOgenius]

no branches are only useful in complex analysis

[@studentscorner4802]

I was looking for the question u left exercise for us

[@mathOgenius]

its in schaums outlines complex analysis

[@samayaparibartan883]

One question - If by making a branch cut, say we are introducing 2 branches w1 & w2. So if we start with a value z belonging to w1, we can never change over to w2. Then how do we go to w2?

[@mathOgenius]

no the branches are already there , we are introducing a branch cut to restrict ourself in one branch.

[@anikdas1760]

Thanks

[@JMaChrisGCarters]

“Functions are not analytic at the branch cut”- why?

[@mathOgenius]

Because after the rotation .. the function changes its value .. that means encounter a jump ..shows discontinuity. hence not analytic

[@JMaChrisGCarters]

Duh okay I’m stupid. So if I choose a different branch cut my function will be analytic at the real line ?

[@mathOgenius]

yes .. of course it will be .. branch cuts are arbitrary..we just take them on x axis for like it's easy to work with that .(and you are not stupid ..nobody is .. everybody is a genius!) :)

[@peterpoli2839]

No no no, sqrt(x) isn’t multivalued

[@amritas2400]

It is. Even in real analysis, sqrt(x) is multivalued. For example, we say that √4 is + or - 2. Because both the square of both positive and negative 2 gives 4. The solution of x^(1/n) has n solutions.

[@bkaanlevent]

iota=i, to the person who does not know what "iota" means