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Analytical Functions

  1. Jun 14, 2008 #1
    1. The problem statement, all variables and given/known data

    Key in writing if possible f (z) with Onley z this mean We can get rid z bar be variable in terms of analytical
    Is there a theory or conclude that Ithbt


    Where was this idea
    Or is the only conclusion
     
  2. jcsd
  3. Jun 14, 2008 #2

    malawi_glenn

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    What?!?!
     
  4. Jun 15, 2008 #3

    Dick

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    I'll back malawi_glenn on that. It's really incoherent. But in x+iy, x and y are two independent variables. In the same way, z and zbar are two independent variables. But you are going to have ask a much clearer question before anyone can even figure out what you are talking about.
     
  5. Jun 15, 2008 #4
    I'm sorry the question is
    Without the use of Kochi - Riemann's equation
    Analytical Function:
    Example:
    [​IMG][/url][/IMG]
     
  6. Jun 15, 2008 #5
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  7. Jun 15, 2008 #6
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  8. Jun 15, 2008 #7
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  9. Jun 16, 2008 #8

    Dick

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    Yes. It's general. d/d(zbar)=0 is the same thing as saying i*d/dx=d/dy using the chain rule for partial derivatives. If you apply that to f=u(x,y)+i*v(x,y) you get the Cauchy-Riemann equations.
     
  10. Jun 16, 2008 #9

    Dick

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    Basically ok. (n*i)^(1/2)=sqrt(n/2)+i*sqrt(n/2). Recheck the sqrt(5i). But remember to be careful how you define 'sqrt' or remember that every nonzero number has two different square roots.
     
  11. Jun 17, 2008 #10
    Good Answer
    Thanks
     
  12. Jun 17, 2008 #11


    (n*i)^(1/2)=sqrt(n/2)+i*sqrt(n/2).

    Excellent
     
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