Originally Posted by

**takis1881** Sorry for my english,i'm greek and i try as much as i can to be clear.

I can see what you mean. I was trying to use Picard's theorem too, but i found something else about the problem. I thought that i could consider that R is not dense in C. So there is an open disk of a point w in C, with no common points with R(range of f) and abs(f(z)-w)>e (e the radius of the disk). Then i consider g(z)=1/(f(z)-w), which is entire because f is entire. But absg(z)<1/e=d and then g(z) is entire and bounded in C, so g is constant(liouville theorem). But if g is constant then f is constant and this is impossible. So R is dense in the complex plane. This is my proof but i don't know if it's correct.

Thanks for helping!!