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2 complex intergrations

  1. Dec 1, 2011 #1
    1. Evaluate ∫C (z)/z2+9 dz , where C is the circle │z-2i│=4.

    what i have done so far is :

    z(t) = 2i + 4eit
    z'(t) = 4ieit
    f(z(t)) = 4ieit/(4ieit)2+9

    ∫ (4ieit/(4ieit)2+9) (4ieit) dt

    intergrate from 0->2pi

    but i dont know how to solve this intergral, can anyone help?

    2. ∫c cos(z)/(z-1)^3(z-5)^2 dz , where C is the circle │z-4│=2.

    this z'(t) = 0
    so , is this intergral equal 0?
    since f(z(t))(z'(t)) = 0


    Thanks
     
  2. jcsd
  3. Dec 1, 2011 #2
    Shouldn't you be using the residue theorem to evaluate the integrals?

    (Note that (1) has poles at ±i3, and (2) has poles at 1 & 5. Which of those lie within the given contours?)
     
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