Oops -- that's *unit* complex numbers, not just complex numbers. Nice geometric questions. --Dan ----- Jim wrote: << Let me be more concrete about this, and phrase this as a puzzle: What is the topology of the set of triples of unit complex numbers (u,v,w) satisfying u+v+w = some fixed complex number z? Clearly all that matters is the magnitude of z, so we might as well assume z is a real positive number; call it r, and let S_r = {(u,v,w): |u|=|v|=|w|=1, u+v+w=r}. If r > 3, S_r is empty; if r = 3, S_r contains just the one point (1,1,1). But what about r < 3? (Quick: Do you think S_r is connected when r = 2.9, or do you think it has two components?)

...

_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele