(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the integral

Given [tex]\int_{C} \frac{e^z}{\pi i - 2z} dz = \int_{C} \frac{e^z}{z-\frac{\pi i}{2}} dz} [/tex]

using Cauchy integral formula.

2. Relevant equations

What I know

[tex]\frac{1}{2\pi i} \int_{C} \frac{f(z)}{z-\zeta} = 2\pi i f(\zeta)[/tex]

3. The attempt at a solution

This in my little girly mind amounts to

[tex]2\pi i f(\frac{\pi i}{2}) = \int_{C} \frac{e^z}{z-\frac{\pi}{2}i} dz \Rightarrow \int_{C} \frac{e^z}{z-\frac{\pi}{2}i} dz = 2 \pi \cdot (i) \cdot (i) = -2\pi[/tex]

But people who are wiser than me says to me "Susanne your result is wrong!". Could someone please point out my mistake?

thanks Susanne

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# Homework Help: Integral calculations using Cauchy's Integral formula

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