# Limit of a complex sequence

1. Oct 16, 2013

### DotKite

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. Oct 16, 2013

### Dick

(1+i)^n is unbounded. But its absolute value is |1+i|^n. What's that??

Last edited: Oct 17, 2013
3. Oct 17, 2013

### DotKite

|1+i|^n = [sqrt(2)]^n?

4. Oct 17, 2013

### Dick

Sure, so can you show the limit of |z_n| is 0? That would show the limit of z_n is also 0.

5. Oct 17, 2013

### DotKite

that is not generally true,

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

{(-1)^n + i/n} does not converge.

6. Oct 17, 2013

### jbunniii

But it is true if the limit is zero. $|z_n| \rightarrow 0$ if and only if $z_n \rightarrow 0$.

7. Oct 17, 2013

oh i see