The question:

Is this a domain?

|Im(z)| > 1

My attempt:

-1 > Im(z) > 1

Therefore it is the region between -1 and 1 on the imaginary axis, thus it is open and connected; i.e. a domain. However, my book states that it is NOT a domain. :/

Why is this so? Thanks.

Edit: Oops, my brain is clearly asleep. It's the region above 1 and below -1, so its not connected. D'oh!