which of the following are true ?
a) There exists non-constant entire function which is bounded on real and imaginary axis.
b) There exists entire function such that $f(0)=1$ and such that $|f(z)|$ is less than or equal to $\dfrac{1}{|z|}$, for all $|z|$ greater than or equal to $5$.
I think for a) $e^{iz^2}$ works. But I have no idea about (b) can I apply Liouville's theorm for (b) or picard's theorm.?
Function is bounded on and outside the disc $|z|=5$. To apply Liouville's theorm we have to prove function is bounded inside $|z|=5$. After this function becomes constant And $f (z) =1$ then I can contradict.
Thanks in advance.