Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Idea

Thread: Factoring a complex function

  1. #1
    Newbie
    Joined
    Jul 2018
    From
    United States
    Posts
    3

    Factoring a complex function

    How can I write the function $f(z)=1-0.7z-0.3z^{-1}$, $z$ complex, as $f^+(z) f^-(z)$, where


    1. $f^+(z)$ is free of zeros and singularities **outside and on** the unit circle
    2. $f^-(z)$ is free of zeros and singularities **inside and on** the unit circle.


    As can be verified, $f$ has a single pole at $z=0$ and two zeros at $z=1$ and $z=3/7$, so I cannot simply take $f^+(z)=f(z)$ and $f^-(z)=1$.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2013
    From
    Lebanon
    Posts
    868
    Thanks
    409

    Re: Factoring a complex function

    $\displaystyle f(1)=f^+(1)f^-(1)=0$

    implies

    $\displaystyle f^+(1)=0$ or $\displaystyle f^-(1)=0$
    Thanks from Archie
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factoring complex trinomials
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Apr 26th 2012, 05:38 PM
  2. Factoring z^4+1 over the complex numbers
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: Mar 1st 2011, 02:09 AM
  3. factoring with complex numbers
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Sep 13th 2009, 07:12 AM
  4. complex factoring problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: May 30th 2008, 07:17 PM
  5. Replies: 3
    Last Post: Nov 5th 2006, 11:02 PM

Search Tags


/mathhelpforum @mathhelpforum