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

  • @xenofurmi
    @xenofurmiАй бұрын

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

  • @ebnenabi6615
    @ebnenabi6615 Жыл бұрын

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

  • @jamesjohn2537
    @jamesjohn2537 Жыл бұрын

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

  • @curtpiazza1688
    @curtpiazza16883 ай бұрын

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

  • Жыл бұрын

    Pure gold! Thank you.

  • @Phi1618033
    @Phi1618033 Жыл бұрын

    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

    @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

    @liboyan7010

    Жыл бұрын

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

  • @chrisjuravich3398

    @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

    @aboringhumanaskssomething

    Ай бұрын

    @@jeremylentz3907 Truly!

  • @crimfan

    @crimfan

    17 күн бұрын

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

  • @mingshuoji445
    @mingshuoji445 Жыл бұрын

    😁The explanation is so elegant !

  • @cbxxxbc
    @cbxxxbc Жыл бұрын

    Dear Prof. Brunton, are there lecture notes/ exercises available that accompany your great lectures?

  • @eduardocarmona8157
    @eduardocarmona81575 ай бұрын

    Awesome! THX

  • @user-js6yn2hc5p
    @user-js6yn2hc5p3 ай бұрын

    Very Nice & Clear Explanations 👌 Thanks professor 🙏

  • @alirezaansari7878
    @alirezaansari7878 Жыл бұрын

    Excellent

  • @nuclearrambo3167
    @nuclearrambo31675 күн бұрын

    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).

  • @skalderman
    @skalderman9 ай бұрын

    Good choice to write forward the solution and decomposing backward

  • @itachi5187
    @itachi518728 күн бұрын

    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?

  • @matejcataric2259
    @matejcataric22592 ай бұрын

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

  • @GIBREABSHAWEL-gk5qr
    @GIBREABSHAWEL-gk5qr9 ай бұрын

    why we add 2pi third always professor

  • @SergeyPopach
    @SergeyPopach6 ай бұрын

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

  • @crimfan
    @crimfan17 күн бұрын

    Roots of Unity should be a math rock band.

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