Is Complex Conjugate Integration Valid on Contour |z|=1?

[hoffmann]

i was thinking this over, and i'd like to know if the following statement is valid:

$$\oint\overline{z}dz$$ = $$\oint1/zdz$$

over the contour $$\left|z\right|=1$$

any thoughts?

 

[lurflurf]

That is obviously true and then some.
In fact z*=z^-1 whenever |z|=1