Complex limit

1. Feb 12, 2008

ehrenfest

[SOLVED] complex limit

1. The problem statement, all variables and given/known data
Evaluate the complex limit if it exists:

$$\lim_{z \to 1} \frac{\log{z}}{z-1}$$

where log denotes the principal branch of the logarithm.

2. Relevant equations

3. The attempt at a solution
I am pretty sure it exists and equals 1, because that is what it equals when I approach with specific sequences. But how can I prove that?

2. Feb 12, 2008

Gib Z

$$\lim_{z \to 1} \frac{\log{z}}{z-1} = \lim_{z\to 0} \frac{\log (1+z)}{z}$$.

Are you allowed to use the property that the series for that log term converges to that log term iff |z| < 1?