$\int_{\gamma}^{} z^{e^{z^{2}}}\, dz$ when $\gamma$ is the unit circle.
complex-analysis
asked 2012-05-10
user id:29282
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What about starting with $z=e^{it}$ and then integrate from $0$ to $2\pi$ What have you tried? – 2012-05-10
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Are you sure you've typed this correctly? Which branch of the power function are you referring to? Note that $z^w$ is not well-defined without stating this. – 2012-05-10
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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