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Homework Help: Limit of a complex sequence

  1. Nov 2, 2013 #1
    1. The problem statement, all variables and given/known data
    a) (1+i)-n as n→∞
    b) n/(1+i)n as n→∞


    2. Relevant equations



    3. The attempt at a solution
    My answers were divergent for both question because (1+i)n=sqrt(2)*en*pi*i/4, so when n→∞, the limit is varying on the circle with radius sqrt(2). But the solution said both of them equal to 0. How can I get that?

    Any help is appreciated.
     
  2. jcsd
  3. Nov 2, 2013 #2

    mfb

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    Staff: Mentor

    Don't forget the minus sign, and the exponent of the magnitude.
     
  4. Nov 2, 2013 #3
    mfb:
    But when the minus is there, the value is still varying, it does not go to infinity in denominator for part a. So I still cannot get the limit equal to 0.
     
  5. Nov 2, 2013 #4

    HallsofIvy

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    There's your error [itex](re^{i\theta})^n= r^n e^{ni\theta}[/itex]. [itex](1+ i)^n= (\sqrt{2})^n e^{n\pi i/4}[/itex]. You did not take the absolute value to the -n powerr.

     
  6. Nov 2, 2013 #5
    Hallsoflvy:
    oh yeah! So sqrt(2)-n→0 as n→∞!?
     
  7. Nov 2, 2013 #6

    HallsofIvy

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  8. Nov 2, 2013 #7
    Thank you so much!
     
  9. Nov 2, 2013 #8

    mfb

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    Staff: Mentor

    That's what I meant with "the exponent of the magnitude.".
     
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