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Math Help - Serious help needed with complex variables

  1. #1
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    Serious help needed with complex variables

    Evaluate the line integral log(z) dz

    where C is the arc defined by z= root2 x e^(itheta), -pi/4 < or = theta < or = pi/4.

    between the points (1-i) and (1+i).


    In a domain where log(z) is analytic we know that d/dz (zlog(z) - z) = log(z).

    Hence evaluate the above integral directly.
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  2. #2
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    We know that d/dz (zlog(z) - z) = log(z).

    If this is true then the integral of log (z) is zlog(z) - z.
    You have the points so:

    [z1log (z1) - z1] - [z2log (z2) - z2]

    where z1= 1 + i and z2= 1 - i
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