Is $f$ is constant ? Yes/No
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
48275
$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
76790
Condition to guarantee $f=0$ on $[a,b]$
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
39386
Harmonic non-surjective functions are constant
106290
Prove a function is constant. (complex analysis)
136011
Must $f$ be continuous?
153411
If $|f|$ is constant, so is $f$ for $f$ analytic on a domain $D$.
23615
Why does zero derivative imply a function is locally constant?
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
105700
Proving $\,f$ is constant.
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
56978
How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?
141863
If the imaginary part of an entire function is never zero, the function is constant
113343
$f$ is constant if derivative equals zero
42075
If $f$ is analytic then $|f|$ is not constant unless $f$ is constant
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?