1)i need an example of a non isolated singularity
2) also i need an entire function which assumes every complex value but the number 1+2i and i want to know the way in order to solve some other questions i have
3) how do i describe the singularity at z= infinity for example at the function f(z)= exp(z)/(z^2 +1) f(z)= (z^2 +1)/exp(z)
4) for f(z) a polynomial =sum (an z^n) of order k can i prove that it has a pole of order k at z=infinity?????
For 1 take something like $$\frac{1}{\sin\left(\frac{1}{z}\right)}$$ For 2, you know that $\exp$ is entire and $\exp(z)\neq 0$, think how that helps.
For 3, you just definie $z=\frac{1}{w}$ and then $z\to \infty$ is the same as $\frac{1}{w}\to 0$. (at least when you go on the real axis)
For 4, just use the definition of a pole of order $k$.