Where is complex Log continuous 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?

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.
