# Math Help - complex question

1. ## complex question

similarly there is another question i am stuck on.

Give an example of a subset E of the complex plane which is connected, neither open nor closed, has nonempty interior, and is unbounded.

I sort of figured out at least for the neither open/closed and unbounded part that perhaps getting the union of a compact set and a non-intersecting open, un-bounded set.

Any suggestions?

2. Originally Posted by shaheen7
similarly there is another question i am stuck on.

Give an example of a subset E of the complex plane which is connected, neither open nor closed, has nonempty interior, and is unbounded.

I sort of figured out at least for the neither open/closed and unbounded part that perhaps getting the union of a compact set and a non-intersecting open, un-bounded set.

Any suggestions?

$\displaystyle{\{\,z\in\mathbb{C}\,\,;\,\,Re(z)\geq 0\,,\,\,0\leq Im(z)<\pi\,\}$

Tonio