If you mean the stem is broken off, you can root stem cuttings & leaves by sticking the stems (or leaf petioles) in a sterile, well-aerated, damp medium, and you can also root leaves by making small cuts across the leaf veins & laying the leaf flat (you might have to pin it flat) on moist soil. It should give you a new plant at each slit. You may need to partially tent the leaf cuttings and/or reduce the leaf volume on the stem cuttings by cutting leaves in half across the veins. Al

I would search for red rex begonias (images) and see if you can find any that match your memory. It does sound like a rex. Dragon Wings is a registered begonia name and is noted for its ever blooming red flowers (and there is a pink blooming one too) and how it holds up in full sun. Angel wing begonias is a common catch all phrase applied to lots of cane type begonias (not rexes).

Is the trunk soft at all? If not, it may be fine. If it is soft then you may have to cut. It looks like it has shot off 2 new branches so it may have sealed itself off. Examine the trunk for softness and let us know. Was the top cut or broken off? If that happens in the future you can seal it with caulk so it won't rot. For the pictures, if you upload to a sharing site like Flikr or Photobucket then you can copy & paste the HTML codes into the message, through the Garden Web editor thing it only allows one at a time. This post was edited by elucas101 on Fri, Mar 1, 13 at 16:10

Yes, Begonia flowers are really weird. (Though I wouldn't rule-out the possibility that you have 2 or more slightly different individuals in your pot.) They make separate male and female flowers on a same plant, and the color intensity can fluctuate from ___? Conditions, PH, temp? IDK, but I've seen it on Begonias that I have. http://science.jrank.org/pages/814/Begonia.html http://www.begonias.org/Articles/Vol47/TuberousBegonias.htm