Complex Limits

**shadow_2145** · September 10th 2008, 01:29 PM

Find the limit of each sequence that converges; if the sequence diverges, explain why.

(1) $z_n = (\frac{1+i}{\sqrt{3}})^n$

(2) $z_n = Log(1 + \frac{1}{n})$

Any help would be appreciated. Thanks!

**topsquark** · September 10th 2008, 04:20 PM

Originally Posted by shadow_2145

Find the limit of each sequence that converges; if the sequence diverges, explain why.

(1) $z_n = (\frac{1+i}{\sqrt{3}})^n$

(2) $z_n = Log(1 + \frac{1}{n})$

Any help would be appreciated. Thanks!

For (1) what is the modulus of
$\frac{1 + i}{\sqrt{3}}$
If this is greater than 1 it diverges. If it is less than 1 the limit is 0.

For (2) what is
$\lim_{n \to \infty} log \left ( 1 + \frac{1}{n}\right )$

-Dan

**11rdc11** · September 10th 2008, 04:52 PM

$z_n = Log(1 + \frac{1}{n})$

To see if it converges,

$\lim_{n \to \infty} Log\bigg(1 + \frac{1}{n}\bigg) = Log(1 + 0) = Log(1)$

$\lim_{n \to \infty}Log(1 + \frac{1}{n}) = 0$

so it converges to 0

Shot went to do something and came back and was too late

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