- #1
Susanne217
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Homework Statement
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.
Homework Equations
What I know
[tex]\frac{1}{2\pi i} \int_{C} \frac{f(z)}{z-\zeta} = 2\pi i f(\zeta)[/tex]
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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