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How to evaluate this in the complex plane?

$\int_{\gamma}^{} z^{e^{z^{2}}}\, dz$ when $\gamma$ is the unit circle.

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    Like mrf said, it is important to choose a branch for the complex logarithm in order for this to be a well-posed problem. However, once this is done I believe that the function in your integral is analytic, so that the integral is zero.2012-05-12

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