What is values of exponential in complex plane I have a doubt about value of $e^{z}$ at $\infty$ in one of my book they are mentioning that as $\lim_{z \to \infty} e^z  \to \infty $
But in another book they are saying it doesn't exist.I am confused now 
As we can see $e^{z}$ is entire function then as $z \to \infty $ then $e^{z}$ must go to $\infty$
Please help.

$|e^{i2\pi n}|=1$  for all $n$  and $|i2\pi n| \to \infty$. So it is not true that $|e^{z}| \to \infty$ as $|z| \to \infty$. Of course the limit is $\infty$ when you take limit through $\{1,2,..\}$ so the limit of $e^{z}$ as $|z| \to \infty$ does not exist. 
