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Homework Help: Partial Fractions but in Complex Analysis

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data

    Use partial fractions to rewrite:


    2. Relevant equations

    3. The attempt at a solution

    I did this:

    (2z)/(z^2+3) = (Az+B)/(z^2+3)

    2z = Az +B

    A = 2, B = 0......problem is that it just recreates the original

    Here is their example in the book:

    1/(z^2+1) = 1/(2i(z-i)) - 1/(2i(z+i))

    I don't understand how they came to their conclusion in their example.

    Any help understanding their example or my question is appreciated.
  2. jcsd
  3. Nov 27, 2011 #2
    factor 1/(z^2+1) as 1/(z+i)(z-i)
    then 1/(z^2+1)= A/(z+i)+ B/(z-i)
    now solve for A and B.... what do you get .
    and then you can do the same trick on your problem
  4. Nov 27, 2011 #3


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    Science Advisor

    Of course it does. You wrote it in exactly the same form. Why would you expect anything else?

    You titled this "Partical fractions but in Complex Analyis"- so use complex numbers:
    [itex]z^2+ 3= (z+ i\sqrt{3})(z- i\sqrt{3})[/itex].

    Your partial fractions should be
    [tex]\frac{2z}{z^2+ 3}= \frac{A}{z+ i\sqrt{3}}+ \frac{B}{z- i\sqrt{3}}[/tex]
  5. Nov 27, 2011 #4
    Thanks guys, oh my gosh

    I actually did their example and set it up all correctly

    I got to the end with A+B=0, A-B=0 and without solving it, it just looked like a contradiction and I didnt realize that B=-1.

    thanks for pointing that out for me, i was like 99% there and got stuck. i hate that
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