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Find where a complex function is differentiable

  1. Mar 14, 2013 #1
    Using the definition of the derivative find at which points the function f(z) = Im(z)/z conjugate is complex differentiable.
    I know that it is not complex differentiable anywhere but I need to show it using the definition and not the Cauchy Riemann equations.
     
  2. jcsd
  3. Mar 14, 2013 #2

    HallsofIvy

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    Write z= x+ iy, so that [itex]f(z)= f(x+ iy)= \frac{y}{x+ iy}= \frac{xy- iy^2}{x^2+ y^2}[/tex] Apply the definition of "differentiable" to that. (It is sufficent to look at the real and complex parts separately.)
     
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