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Homework Help: Complex integration over a curve

  1. Mar 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Compute ∫C (z+i)/(z3+2z2) dz

    2. Relevant equations
    C is the positively orientated circle |z+2-i|=2


    3. The attempt at a solution
    I managed to solve a similar problem where the circle was simply |z|=1, with the centre at the origin converting it to z=e with 0≤θ2∏. I'm not sure how to go forward with the centre in another position.

    If I want to parametise the equation for z for the circle, then I get two different equations for z because of the possibilty that it could be + or - because of the absolute value.

    I haven't gotten very far - could anyone help start me off on this!
     
    Last edited: Mar 10, 2013
  2. jcsd
  3. Mar 10, 2013 #2

    HallsofIvy

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    Science Advisor

    |z+ 2- i|= 2 is the same as |z- (-2+ i)|= 2 and is the circle with center at -2+ i and radius 2 with [itex]\theta[/itex] going from 0 to [itex]2\pi[/itex]. Yes, we can write the circle with center at 0 and radius 1 as [itex]z= e^{i\theta}[/itex]. The circle with center at 0 and radius 2 is [itex]z= 2e^{i\theta}[/itex]. Finally, the circle with center -2+ i and radius 2 is [itex]z= -2+ i+ 2e^{i\theta}[/itex]
     
  4. Mar 10, 2013 #3
    Thank you, that helps!
     
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