Find all possible values of

$\displaystyle \int_{\gamma } \frac{1}{1+z^2}dz$ where $\displaystyle \gamma$ is some path joining 0 to 1 which is in the domain of $\displaystyle f(z) = \frac{1}{1+z^2}$.

Any help would be great. Thanks!

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- Oct 14th 2010, 07:16 PMmathmaniac234Complex Domains and Paths
Find all possible values of

$\displaystyle \int_{\gamma } \frac{1}{1+z^2}dz$ where $\displaystyle \gamma$ is some path joining 0 to 1 which is in the domain of $\displaystyle f(z) = \frac{1}{1+z^2}$.

Any help would be great. Thanks! - Oct 15th 2010, 07:31 AMKatyCar
Would the idea of independence of path help in this situation?