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Thread: Complex Integration

  1. #1
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    Complex Integration

    Use the definition to compute the following integral:


    $\displaystyle \int_C e^z$ where $\displaystyle C$ is the contour from $\displaystyle 1-i$ to $\displaystyle 1+i$.

    I do not see how to do this problem. I know the definition is $\displaystyle \int_C f(z)dz = \int_C f(z(t))z'(t)dt$. However, I don't see how to use it in this problem. Thanks.
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  2. #2
    MHF Contributor chisigma's Avatar
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    The function $\displaystyle e^{z}$ is analytic $\displaystyle \forall z \in \mathbb{C}$, so that the integral...

    $\displaystyle \int_{A}^{B} e^{z} \cdot dz$

    ... doesn't depend from the path connecting A with B...

    ... what is the simplest path from $\displaystyle 1 - i$ to $\displaystyle 1+i$?...

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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