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Limit of a complex sequence

  • Thread starter DotKite
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  • #1
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Homework Statement



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

Homework 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.
 

Answers and Replies

  • #2
Dick
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Homework Statement



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

Homework 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.


(1+i)^n is unbounded. But its absolute value is |1+i|^n. What's that??
 
Last edited:
  • #3
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(1+i)^n is unbounded. But its absolute value is |1+i|^n. What's that??
|1+i|^n = [sqrt(2)]^n?
 
  • #4
Dick
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|1+i|^n = [sqrt(2)]^n?
Sure, so can you show the limit of |z_n| is 0? That would show the limit of z_n is also 0.
 
  • #5
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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.
that is not generally true,

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

{(-1)^n + i/n} does not converge.
 
  • #6
jbunniii
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that is not generally true,

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

{(-1)^n + i/n} does not converge.
But it is true if the limit is zero. ##|z_n| \rightarrow 0## if and only if ##z_n \rightarrow 0##.
 
  • #7
81
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oh i see
 

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