Complex Analysis L05: Roots of Unity and Rational Powers of z

[@xenofurmi]

This series is so great. We all really appreciate it!

[@ebnenabi6615]

I literally love you. (: I wish God helps you throughout your life as you have helped many. I hope you success, Steve.

[@jamesjohn2537]

This another great lesson sir, thanks it spikes my curiosity to love mathematics and need to learn more!!

[@dantemlima]

I´ve been binge watching all your lectures to complement an introductory course on complex analysis I´m taking on Coursera that unfortunately is not completely inteligible. Congratulations on your didactics and contagious enthusiasm with the theme. Thank you for the time and effort put into your video classes. Those students that may have instruction live with you are surely in luck. Keep up the good work for those of us on the other side of the screen.

[@DeathByDegrees8]

Thank you for these incredible videos! I never took complex formally but learned it in my engineering classes so this deep dive is a very nice watch

[@curtpiazza1688]

Love your phrase..."the mathy way of saying it". 😂 Great informative video! 😊

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Videos like this prove that we're at the point in human history where your college tuition is only paying for a piece of paper to hang on your wall, because you can get an entire, quality university education on KZbin. And you don't even need to leave your house to do it.

[@jeremylentz3907]

This is supplementary material for me that happens to be higher quality than most of my university professors. He and professor Leonard is who i should really be paying 10s of thousands of dollars.

[@liboyan7010]

@@jeremylentz3907 the lectures from Steve Brunton are totally great!!!

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I feel like I am stealing by watching a lecture like this for free. I am sitting in on this brilliant professor’s class without paying a single penny.

[@aboringhumanaskssomething]

@@jeremylentz3907 Truly!

[@crimfan]

In terms of lecture quality, sure, but that’s not only what a good uni instructor does.

[@dantemlima]

Roots of Unity = great name for a rock band!

[@MohammadrezaParsa-k7p]

Very Nice & Clear Explanations 👌 Thanks professor 🙏

Pure gold! Thank you.

[@mingshuoji445]

😁The explanation is so elegant !

[@eduardocarmona8157]

Awesome! THX

[@skalderman]

Good choice to write forward the solution and decomposing backward

[@Alireza_Ansaree]

Excellent

[@karthicksk8793]

Thanks a lot ❤

[@crimfan]

Roots of Unity should be a math rock band.

[@nuclearrambo3167]

suposse we have a discrete time signal x[n]=exp(jwn) and it is periodic with N. then exp(jw(n+N))=exp(jwn) thus exp(jwN)=1. because 1=exp(2(pi)k) where k is an integer, equation w=2(pi)k/N must hold. if N is chosen to be pi ,which is not an integer, x[n] is not periodic. consequently, has infinitely many unique values. In addition, for x[n] to be periodic, w must be some multiple of pi (true when k and N are integers).

[@SergeyPopach]

phase angle could be represented as zero and this Log equation would be still valid

[@matejcataric2259]

21:10 m can be from Z,but n can not be from Z,because m/0 is not defined.

[@itachi5187]

if the phase angle is getting increased that totally understand but then how can the z value remains same because if i visualize it then it will be like the position of z is shifting in a 3 dimentional plain. Sir can you explain this?

[@GIBREABSHAWEL-gk5qr]

why we add 2pi third always professor