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Complex Functions

  1. Jun 12, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the limit :

    [​IMG]
    [​IMG]


    3. The attempt at a solution
    [​IMG]
    1. The problem statement, all variables and given/known data






    result


    3. The attempt at a solution
     
  2. jcsd
  3. Jun 12, 2008 #2
    Last Qiustion::biggrin:
    [​IMG]
     
  4. Jun 15, 2008 #3
    please wait:zzz:
     
  5. Jun 16, 2008 #4

    Dick

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    cos(pi/2)+i*sin(pi/2)=i, not i^(1/2). ???
     
  6. Jun 16, 2008 #5

    Dick

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    But what? Isn't the limit still 1?
     
  7. Jun 17, 2008 #6
    By imposing
    I said let w=i===>w^2=-1
     
  8. Jun 17, 2008 #7
    Yes,
    Find this limit
     
  9. Jun 17, 2008 #8

    Dick

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    I don't understand that at all.
     
  10. Jun 17, 2008 #9

    Dick

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    Substitute zbar for z in the power series. What's wrong with that?
     
  11. Jun 17, 2008 #10
  12. Jun 17, 2008 #11

    Dick

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    It doesn't have to be analytical. You've shown using the series (or l'Hopital) that if z_n is a series of complex numbers approaching 0, then sin(z_n)/z_n->1. z_n* is also a series of complex numbers approaching 0. The series expansion holds for ANY z.
     
  13. Jun 17, 2008 #12
    Like this
    [​IMG]
     
  14. Jun 17, 2008 #13
    Infact:
    [​IMG]
    delta=???
     
  15. Jun 17, 2008 #14

    Dick

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    Sure. |(sin(z*)/z*|=|sin(z)/z|. Because (sin(z)/z)*=(sin(z*)/z*) and |z|=|z*|. So you don't need analyticity, correct?
     
  16. Jun 17, 2008 #15
    Dear: Dick
    correct 100%.


    Thank you for answering me
    Thank you very much:blushing:
    In Arabic:
    :biggrin:شكرًا جزيلاً
     
  17. Jun 17, 2008 #16

    Dick

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    Sure. Sorry, I'm not good at the script. afwan.
     
  18. Jun 17, 2008 #17
    O. My Dod
    afwan:surprised
    very very Excellent
    Rather than to learn English
    You have learned Arabic
     
  19. Jun 17, 2008 #18

    Dick

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    shukran, afwan, is about as far as I go. Oh, and salam alekum. That's it. I don't even remember how to count, even though this is a math site. So you might want to keep learning english. :)
     
    Last edited: Jun 17, 2008
  20. Sep 24, 2008 #19
    show that :
     
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