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Show that this function is analytic

  1. Mar 14, 2006 #1
    Show that this function is analytic

    [tex] \left( x + \frac{x}{x^2 + y^2} \right) + i \left( y - \frac{y}{x^2 + y^2} \right) [/tex]

    now... would i substitute [tex]x = \frac{z + \overline{z}}{2} [/tex]
    [tex] y = \frac{z - \overline{z}}{2} [/tex]

    and then see if z or z bar appear exlicitly in the function??
    Would that solve it??

    Is there an easier way? A less Messy way?
  2. jcsd
  3. Mar 15, 2006 #2


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    If I recall correctly, a function is analytic if it is differentiable and if it satisfies the Cauchy-Riemann equations, perhaps you should check those?
  4. Mar 15, 2006 #3
    is there another way of doing it... perhaps using the substitutions i suggested above and then checking the domain of the function?
  5. Mar 15, 2006 #4
    Using the Cauchy-Riemann equations is probably the easier way.
  6. Mar 15, 2006 #5
    Your equation for y should be over 2i not just 2.
  7. Mar 16, 2006 #6


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    There are complex functions whose domain is C but are nowhere analytic.
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