Partial fractions

  • Thread starter jameson2
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  • #1
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I'm trying to do a question that requires the expansion of the following using partial fractions:
[tex]f(z)=\frac{1}{(1+z^3)^2}[/tex].
The fact that the bottom is squared is throwing me off for some reason... I've factorized the bottom, but I'm not sure whether I should use the complex roots or not, or even if it's possible without using complex roots.
Any help would be appreciated.
 

Answers and Replies

  • #2
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Hey there,
The trick is to use identity 1+Z^3=(1+z)(1-Z+Z^2) and then just square this expression and do the partial fraction as usual.
Hope this helps:)))
 
  • #3
HallsofIvy
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[tex]\frac{1}{(1+z^3)^2}= \frac{1}{(z+1)^2(z^2-z+1)^2}[/tex]
and can be written as "partial fractions" as
[tex]\frac{A}{z+1}+ \frac{B}{(z+1)^2}+ \frac{Cx+D}{z^2- z+1}+ \frac{Ex+F}{(z^2- z+1)^2}[/tex]

There was an earlier question about the "principal part" or "Laurent series" for [itex]1/(z^2+1)^2[/itex] which I answered by reducing to partial fractions with complex coefficients. Is this related to that thread?
 
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