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Range of z+1/z (complex function)

  1. Mar 9, 2009 #1

    gop

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

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

    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
    [tex]z=1/2(w+-sqrt(w^2-4))[/tex] where especially the w^2-4 term makes it difficult to say what really happens.

    thx
     
    Last edited: Mar 9, 2009
  2. jcsd
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