If $f$ is analytic and $3\operatorname{Re}f+2\operatorname{Im}f$ is constant, is $f$ also constant?
62640
Show a given analytic function is constant
96539
is $f$ constant or dilation
118096
If $f^2$ and $f^3$ are smooth, does it follow that $f$ is smooth?
18877
$f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic
9844
Proof composition of analytic functions is analytic
104369
If $f$ continuous and $f(x^2) = f(x)$, then $f$ is a const
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
84103
Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
132663
Show $f$ is analytic if $f^8$ is analytic
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
28120
Are intervally constant analytic functions always constant?
96050
$f$ an analytic function on $\mathbb{C}$ which takes values in $\mathbb{C}\backslash(-\infty,0]$ implies constant
39921
show that f is constant on I
85750
If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?
106175
A function is analytic if and only if it is holomorphic
148474
on the boundary of analytic functions