# Thread: ln z - continuous, holomorphic(analytic)

1. ## ln z - continuous, holomorphic(analytic)

Showing that ln z is analytic in $\displaystyle Re \leq 0$ I used CR-equations. I guess that's sufficient since a function needs to be analytic to satisfy C-R equations.
I'm also supposed to show that ln z is discontinuous in $\displaystyle Re < 0$ Briefly: I showed that $\displaystyle -\pi, \pi$ hits the same point if the radius is the same.

Now to my question, not a part of the exercise, but I like to know. How can I show that ln z is continuous in for instance $\displaystyle Re > 0$ I have another thread about continuous functions, but that's a more general prof. I like to put get together an example with some help from you folks.

2. It turns out I misunderstood the exercise somewhat. I had to show that ln z is analytic in the whole complex plane, but the negative real part. This expression got the better of me. $\displaystyle \Omega = \mathbb{C}$ \ $\displaystyle \{z | z \in \mathbb{R}, z \leq 0 \}$