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Math Help - Contour Integral - I've done it but not sure if i'm correct.

  1. #1
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    Contour Integral - I've done it but not sure if i'm correct.

    Compute \int_C \bar{z} dz where C is the circle |z|=2 traversed three times, clockwise.

    ok, so just wondering if i have done this correctly?

    z(t)=2e^{-\pi i t} , 0 \leq t \leq 6

    \bar{z} = 2e^{\pi i t}

    dz= -2i\pi e^{-\pi i t}

    \int_C \bar{z} dz = \int_0^6 (2e^{\pi i t})(-2i\pi e^{-\pi i t})dt

    -4\pi i [t \big|_0^6

    -24\pi i
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    Re: Contour Integral - I've done it but not sure if i'm correct.

    It looks fine
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