# Thread: Complex Limits

1. ## Complex Limits

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

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

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

Any help would be appreciated. Thanks!

2. Originally Posted by shadow_2145
Find the limit of each sequence that converges; if the sequence diverges, explain why.

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

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

Any help would be appreciated. Thanks!
For (1) what is the modulus of
$\displaystyle \frac{1 + i}{\sqrt{3}}$
If this is greater than 1 it diverges. If it is less than 1 the limit is 0.

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

-Dan

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

To see if it converges,

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

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

so it converges to 0

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