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suppose $I_r= \int dz/(z(z-1)(z-2))$ along $C_r$, where $C_r = \{z\in\mathbb C : |z|=r\}$, $r>0$. Then

  1. $I_r= 2\pi i$ if $r\in (2,3)$

  2. $I_r= 1/2$ if $r\in (0,1)$

  3. $I_r= -2\pi i$ if $r\in (1,2)$

  4. $I_r= 0$ if $r>3$.

I am stuck on this problem . Can anyone help me please...... I can't solve it with residue theorem......

I don't know where to begin?

  • 2
    Where are the poles? Around each pole that within the circle of radius $r$, assuming you are integrating CCW, you get the residue of the pole, times $2\pi i$. Remember that the residue is the value of the rest of the function at the pole, if you ignore the factor that is going to infinity. What do you get when you try that?2012-12-18
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    By the residue theorem all option are looking wrong. Am I right????????/2012-12-18

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