Complex Analysis L05: Roots of Unity and Rational Powers of z
Ғылым және технология
This video explains how to use the complex Logarithm, Log(z), and the exponential to compute fractional/rational powers of complex numbers. A special case are the n-th roots of the number 1, or the square root of i, etc...
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This video was produced at the University of Washington
Пікірлер: 23
This series is so great. We all really appreciate it!
I literally love you. (: I wish God helps you throughout your life as you have helped many. I hope you success, Steve.
This another great lesson sir, thanks it spikes my curiosity to love mathematics and need to learn more!!
Love your phrase..."the mathy way of saying it". 😂 Great informative video! 😊
Pure gold! Thank you.
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 KZread. And you don't even need to leave your house to do it.
@jeremylentz3907
Жыл бұрын
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
Жыл бұрын
@@jeremylentz3907 the lectures from Steve Brunton are totally great!!!
@chrisjuravich3398
Жыл бұрын
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
Ай бұрын
@@jeremylentz3907 Truly!
@crimfan
17 күн бұрын
In terms of lecture quality, sure, but that’s not only what a good uni instructor does.
😁The explanation is so elegant !
Dear Prof. Brunton, are there lecture notes/ exercises available that accompany your great lectures?
Awesome! THX
Very Nice & Clear Explanations 👌 Thanks professor 🙏
Excellent
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).
Good choice to write forward the solution and decomposing backward
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?
21:10 m can be from Z,but n can not be from Z,because m/0 is not defined.
why we add 2pi third always professor
phase angle could be represented as zero and this Log equation would be still valid
Roots of Unity should be a math rock band.