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Math Help - how can write this expression in z=x+yi

  1. #1
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    how can write this expression in z=x+yi

     f(z)=tan^{-1}(\frac{2xy}{x^{2}-y^{2}})-iln(|z|^{2})

    how can we write f(z) in terms of z.
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  2. #2
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    Hints. (1) If z = x + iy then z^2 = x^2-y^2 + 2xyi.

    (2) If w = u + iv then \arg w = \tan^{-1}\bigl(\tfrac vu\bigr) \pm \pi.

    (3) If w = u + iv then \log w = \log|w| + i\arg w.
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  3. #3
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    mm

    mm. i got :

     arg(z^{2}) - i log (|z|^{2})

    can it be any simpler?
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  4. #4
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    Quote Originally Posted by szpengchao View Post
    mm. i got :

     arg(z^{2}) - i log (|z|^{2})

    can it be any simpler?
    Yes. That was the point of hint 3.
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