I asked this troubling question a few weeks ago, ever since then, and talking with other people, turns out that the problem is salvageable, but it has to be change to make sense. So I was wondering, should I just post the new version with the proof as an answer, if ever someone comes across it?, or should I post a new question and answer it myself?, what should I do?
I would suggest to post a new question, and then post an answer yourself. I would add a link to the previous question ("See also ..."), and in the old version, I would add at the end a link to the new one ("Related: ...").
Probably you will end up accepting your own answer, but I would wait a couple of days before doing that, in case someone else wants to contribute a different approach.
Also, in case there may be confusion, you may want in the body of the question to be explicit about how the new version you are posting is not a duplicate of the old one.
Since answers were already given to the original form of the question, you should not rewrite the question itself.
If you wish, you can post a self-answered question if you think the corrected version may be of interest to others. But check if it's not been asked before... most basic questions about roots in the complex plane probably exist on the site already.