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Math Help - complex analysis integration

  1. #1
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    complex analysis integration

    can anyone explain to me the parameterization of the semi circle on this page

    Contour Integral

    like why is it -cos(t) + isin(t) as opposed to just cos(t) + isin(t).

    Thank you.
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  2. #2
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    Because you are going the other way (look at the arrows).
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  3. #3
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    thanks

    but why is the cosine negative and not the sine?

    shouldn't the direction affect both sine and cosine?
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  4. #4
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    Oh, that is because you are taking the conjugate.
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  5. #5
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    i mean, right before you find the conjugate. initially, it is

    -cos (t) + isin (t). Thats the part I dont understand. Why is the cosine negative and the sine positive.

    I understand the conjugate of that becomes

    - cos (t) - isin (t).
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