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Complex analysis

  1. Feb 12, 2007 #1
    Can anyone give me some advice on how to solve this problem?

    in the reflection principle if f(x) is pure imaginary then the conjugate of f(z)=-f(z*) where z* is the complex conjugate of z.

    Any advice on where to start?

    thanks
     
  2. jcsd
  3. Feb 12, 2007 #2
    sorry I posted in the wrong forum
     
  4. Feb 13, 2007 #3

    Dick

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    I assume 'f(x) pure imaginary' means pure imaginary along the real axis. In which case you might want to consider g(z)=i*f(x). What kind of a function is g on the real axis?
     
  5. Feb 13, 2007 #4
    I'm assuming that they simply are asking for a graphic representation of this problem. In which case simply draw the imaginary part of z, which is simply a perpendicular line from the real axis to the point z, and z* would simply be the perpendicular line from the real axis in quadrant 4 of the Cartesian coordinate system.
     
  6. Feb 13, 2007 #5

    Dick

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    ?????? I have no idea what that is supposed to mean. The problem is, in fact, about extending the domain of definition of an analytic function. rbzima, aren't you supposed to be working on group theory?
     
  7. Feb 13, 2007 #6
    How is this a problem (I see no (implicit) question mark)?
     
  8. Feb 13, 2007 #7

    Dick

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    He's stating a variant of the Schwarz reflection principle. And trying to prove it.
     
  9. Feb 13, 2007 #8
    LOL - This caught my attention, but I managed to finish my group theory stuff. Forgive me if I was wrong, but you don't really have anything to "solve" using what you stated. If f(x) is pure imaginary, it will exist on the imaginary axis, and it's conjugate will then exist on the imaginary axis as well. Maybe I'm just reading the question wrong.
     
  10. Feb 13, 2007 #9

    Dick

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    Look up the reflection principle and then read the question again. He wrote f(x) is pure imaginary. He didn't write that f(z) is. This is intended as f(x) is imaginary when x is real. Purely imaginary analytic functions are pretty trivial.
     
  11. Feb 13, 2007 #10
    The problem states:
    Find the Radius of Convergence of the following Power Series:
    (a) ∑ as n goes from zero to infinity of Z^n!
    (b) ∑ as N goes from zero to infinity of (n + 2^n)Z^n

    For (a) I think the radius of convergence is 1 but I'm a bit unsure of that...
     
  12. Feb 13, 2007 #11

    Dick

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    You are clearly in the wrong thread.
     
  13. Feb 13, 2007 #12
    Thanks everyone I think I figured it out
     
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