Thanks for the answers, they really got me thinking and I just came up with an idea; now i do not know if its valid or logical in all its statements, but maybe you can tell me if it is..
I can rewrite.
e^{z/\overline{z}}
as
e^{z^2/\left|z\right|^2}
then i get:
\oint_{|z|=r}...
Im doing some complex variable "counter integration" problems and this one came up.
I = \oint e ^{\frac{z}{\overline{z}}}dz
the integral must be done over a circle with radio r
My first attempt was to do it in the exponetial form, so we have this:
\frac{z}{\overline{z}} =...