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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


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  4. Jun 15, 2008 #3


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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:
  6. Jun 15, 2008 #5
  7. Jun 15, 2008 #6
  8. Jun 15, 2008 #7
  9. Jun 16, 2008 #8


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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


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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
  12. Jun 17, 2008 #11


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