1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

    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


    User Avatar
    Homework Helper

    There are complex functions whose domain is C but are nowhere analytic.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook