So we need to show f = exp(z) (1+x^2) + z is surjective to the complex plane.

F maps [- oo , oo ] to [- oo , oo ].

Also conj(f(z)) = f(conj(z)).

Hence f is surjective on the reals.

By picard if f(z) =\= L then this L is unique.

But by the above f(conj(z)) =\= conj L.

Hence contradicting picard.

Therefore f is surjective to the complex plane.

So the singularities of its super are bounded.

Q.E.D.

Regards

Tommy1729

F maps [- oo , oo ] to [- oo , oo ].

Also conj(f(z)) = f(conj(z)).

Hence f is surjective on the reals.

By picard if f(z) =\= L then this L is unique.

But by the above f(conj(z)) =\= conj L.

Hence contradicting picard.

Therefore f is surjective to the complex plane.

So the singularities of its super are bounded.

Q.E.D.

Regards

Tommy1729