Where is complex Log continuous

Question

Write down the biggest subset $D$ of $\mathbb C$ on which ${\rm Log(z)}$ is a continuous function. Explain why ${\rm Log(z)}$ is not continuous at points outside $D.$

Anyone know the answer to this?

My answer here: http://math.stackexchange.com/questions/88341/branch-cut-and-logz-derivative/88358#88358 might help... — Elchanan Solomon, Apr 18 '12 at 14:38

score 2 · Answer 1 · edited Apr 18 '12 at 14:36

2

I'll tell you one possible answer, and you tell me why (I'm assuming the principal branch):

Answer: $D$ is the complex plane minus the non-positive reals.

Hint: Follow things in a semi-circle and observe the "jump" in angles.

edited Apr 18 '12 at 14:36

J. M. ain't a mathematician

75,051

answered Apr 18 '12 at 14:33

Alex Youcis

54,059

Where is complex Log continuous

1 Answers1