# Math Help - Complex analysis, Cauchy's integral theorem

1. ## Complex analysis, Cauchy's integral theorem

Use cauchy's integral formula to evaluate
$\oint \frac{e^{sin(z)}}{z^2(z-\frac{\pi}{4})}$

over the curve,
$c:=|z|=\frac{\pi}{8})$

Okay, so i used the method shown in lectures,

Since the only singularity inside C is for z=0,

we let ,

$f(z)=\frac{e^{sin(z)}}{(z-\frac{\pi}{4})}$

hence, by cauchy's formula, z=0

$(2\pi i).\frac{e^{sin(0)}}{(0-\frac{\pi}{4})}= -8i$

Since the only singularity inside C is for z=0, we let , $f(z)=\frac{e^{sin(z)}}{(z-\frac{\pi}{4})}$ hence, by cauchy's formula, z=0 $(2\pi i).\frac{e^{sin(0)}}{(0-\frac{\pi}{4})}= -8i$
It should be $2\pi i f'(0)$ , not $2\pi i f(0)$ .