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Math Help - some complex variables

  1. #1
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    some complex variables



    As you can see from the checkmarks I already got 6a and 4
    If someone could just help me with the notation on 1, like what do those (+) things mean?

    original link: http://www.math.ualberta.ca/~runde/files/ass411-2.pdf
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  2. #2
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    I'm pretty sure that's just a polygonal path (straight-line) path from the points 1,i,-1,-i,1. Looks pretty messy too.
    If I calculate an antiderivative:

    \int_0^{1}\frac{1}{z+t}dt=\text{Log}\left(\frac{z+  1}{z}\right)

    and then use this to calculate the other integral, I get for the first leg:

    \mathop\int\limits_{L_1}\frac{1}{z}dz=\frac{-1+i}{i-1}\text{Log}\left(\frac{\frac{1}{i-1}+1}{\frac{1}{i-1}}\right)=\pi/2 i

    Maybe easier way though.
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  3. #3
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    well one thing i just thought of is, this is a closed piecewise smooth curve so wouldn't the integral be 0?
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  4. #4
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    Quote Originally Posted by jbpellerin View Post
    well one thing i just thought of is, this is a closed piecewise smooth curve so wouldn't the integral be 0?
    No. The integral is zero only if the integrand is analytic in and on a closed contour and 1/z is not in any closed contour about the origin.
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