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Math Help - Complex number

  1. #1
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    Unhappy Complex number

    /z/=1 and w=(z-1)/(z+1) [where z not equal to -1], then find Re(w).
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  2. #2
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    Quote Originally Posted by matsci0000 View Post
    /z/=1 and w=(z-1)/(z+1) [where z not equal to -1], then find Re(w).
    Here is a hint: w = \frac{{z - 1}}{{z + 1}} = \frac{{z\overline z  + z + \overline z  - 1}}{{\left| {z + 1} \right|^2 }}
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  3. #3
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    Hi

    |z| being equal to 1, you can let |z| = e^{i\theta}

    Then \frac{z-1}{z+1} = \frac{e^{i\theta}-1}{e^{i\theta}+1}

    \frac{z-1}{z+1} = \frac{e^{i\frac{\theta}{2}}(e^{i\frac{\theta}{2}}-e^{-i\frac{\theta}{2}})}{e^{i\frac{\theta}{2}}(e^{i\fr  ac{\theta}{2}}+e^{-i\frac{\theta}{2}})}

    Can you go on now ?

    EDIT : too late ...
    Last edited by running-gag; September 4th 2009 at 09:20 AM. Reason: too late
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