How to Evaluate the Integral of dz/(2+z*) for C Given by z=1?

[pone]

Homework Statement

evaluate :

integral of closed curve dz/(2+z*) (sorry for the lack of syntax
where C is given by z=1

Homework Equations

Cauchy's integral formula

The Attempt at a Solution

I believe I have to change the denominator in terms of z rather than z*, but I do not know how. Any help?

 

[Count Iblis]

z* is not an analytic function of z, however if z is on the unit circle, then you can find a suitable analytic expression for z* in terms of z (which is then only valid on the unit circle).

Hint: consider the expressions of z and z* in polar coordinates.