Complex Analysis: Line Integrals

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Homework Statement


I have a problem as follows:
Let [tex]\gamma=\beta+[e^2\pi,1][/tex] where [tex]\beta[/tex] is given by [tex]\beta(t)=e^{t+it}[/tex] for [tex]0\leq 2 \leq \pi[/tex]. Evaluate [tex]\int_\gamma z^{-1} dz[/tex] .




Homework Equations





The Attempt at a Solution


I know that I need to parameterize the path and I have come up with the path as [tex][e^2\pi,1][/tex]. I also know that I need to integrate this problem along the path and then integrate the function and add the parts together. However, I can't seem to come up with the right way to accomplish this task. I will appreciate your help. Thank you.
 

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