# Range of z+1/z (complex function)

1. Mar 9, 2009

### gop

1. The problem statement, all variables and given/known data

Give the range of the function
$$f(z)=z+1/z$$
$$z \in \mathbf{C} , Im(z)>0$$

2. Relevant equations

3. The attempt at a solution

tried to use polar form to either seperate real and imaginary part or get r*exp(I*phi) both failed to yield suitable closed form expressions. Also tried to just solve w=z+1/z which gives
$$z=1/2(w+-sqrt(w^2-4))$$ where especially the w^2-4 term makes it difficult to say what really happens.

thx

Last edited: Mar 9, 2009