# Integrating the Complex conjugate of z with respect to z

Im doing a bit of contour integration, and a question came up with a term in it am unsure of how to do: in its simplest form it would be

$$\int$$$$\bar{z}$$dz

where z is a complex number and $$\bar{z}$$ is it's conjugate. Hmm i can't get the formatting to work out properly.. :S

Last edited:

Dick
Homework Helper
If you are integrating over a circular contour of radius R then zz*=R^2, so z*=R^2/z. Otherwise you just have to take the contour and write it as z=(x(t)+iy(t)), so z*=(x(t)-iy(t)).

Well now i feel kind of stupid... its line intergration, not contour integration :P the question reads:

Evaluate the integral:

$$\int$$( $$\bar{z}$$ +1 ) dz
L

Where L is the line segment from -i to 1+i.

normally i would just integrate and sub in start and end point, but i have totaly drawn a blank on what to do with the conjugate in this case...

Dick