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Math Help - one last question.

  1. #1
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    one last question.

    I just can't figure this one out (at all). ANY help would be appreciated:

    Let C be the circle of centre 0 and radius 10, oriented counterclockwise. For the function f(z)=\frac{sin(z)}{z(z-3i)(z-30i)} , find \int_C f(z) \,dz .
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by MathSucker View Post
    I just can't figure this one out (at all).f ANY help would be appreciated:

    Let C be the circle of centre 0 and radius 10, oriented counterclockwise. For the function f(z)=\frac{sin(z)}{z(z-3i)(z-30i)} , find \int_C f(z) \,dz .
    Use the residue theorem.

    Note that both poles are simple!

    \int_Cf(z)dz=2\pi i \sum res(f)=2\pi i\left( \frac{\sin(0)}{(-3i)(-30i)}+\frac{\sin(3i)}{(3i)(3i-30i)}\right)=...
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