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Residue Theorem

  1. Oct 5, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the residue of ##\oint { \frac { sinz }{ 2z-\pi } } dz## where ##\left| z \right| =2##

    2. Relevant equations

    ##f\left( z_{ o } \right) =\frac { 1 }{ 2\pi i } \oint { \frac { f\left( w \right) }{ w-z_{ o } } } dw##

    3. The attempt at a solution

    It seems to me that the answer is ##2\pi i##, but the book gives ##\pi i##.

    Not sure what I did wrong, I am pretty confident in my answer.

  2. jcsd
  3. Oct 5, 2014 #2


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    Gold Member

    For your integral, [itex] f(z_0)=\frac 1 2 \sin \frac \pi 2 [/itex] and [itex]z-z_0=z-\frac \pi 2 [/itex].
  4. Oct 5, 2014 #3
    I got [itex]\pi i[/itex] as well. You probably forgot a factor of half when calculating the residue.
  5. Oct 5, 2014 #4
    Where does the 1/2 factor come from?

  6. Oct 5, 2014 #5
    Never mind, I see that it the bottom needs to have a two factored out to fit the form.

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