1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    2016 Award

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Staff Emeritus
    Science Advisor

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

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That's what I meant with "the exponent of the magnitude.".
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Limit of a complex sequence
  1. Limit of a Sequence (Replies: 18)

  2. Limits and Sequences (Replies: 8)

  3. Limit of a Sequence (Replies: 1)

Loading...