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Limit of a complex sequence

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data

    find the limit z_n = [(1+i)/sqrt(3)]^n as n -> ∞.

    2. Relevant equations



    3. The attempt at a solution

    Apparently the limit is zero (via back of the book), but I have no clue how they got that answer.

    (1 + i)^n seems to be unbounded, thus i do not see how z_n can go to zero I am lost.
     
  2. jcsd
  3. Oct 16, 2013 #2

    Dick

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    (1+i)^n is unbounded. But its absolute value is |1+i|^n. What's that??
     
    Last edited: Oct 17, 2013
  4. Oct 17, 2013 #3
    |1+i|^n = [sqrt(2)]^n?
     
  5. Oct 17, 2013 #4

    Dick

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    Sure, so can you show the limit of |z_n| is 0? That would show the limit of z_n is also 0.
     
  6. Oct 17, 2013 #5
    that is not generally true,

    take |(-1)^n + i/n| which converges to 1

    {(-1)^n + i/n} does not converge.
     
  7. Oct 17, 2013 #6

    jbunniii

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    But it is true if the limit is zero. ##|z_n| \rightarrow 0## if and only if ##z_n \rightarrow 0##.
     
  8. Oct 17, 2013 #7
    oh i see
     
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