- #1

- 317

- 0

## 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

Last edited: