$f$ and $|f|$ are analytic.
42075
If $f$ is analytic then $|f|$ is not constant unless $f$ is constant
55347
for two non zero complex polynomial $p(z),q(z)$ we have $p(z)\overline{q(z)}$ is analytic if and only if ?? CSIR - June $2013$
43177
How do I rigorously show $f(z)$ is analytic if and only if $\overline{f(\bar{z})}$ is?
32723
Open sets and holomorphic functions in Complex analysis
63446
The existence of analytical branch of the logarithm of a holomorphic function
80421
Show that $a - b \mid f(a) - f(b)$
62901
Bound for Analytic Function on Unit Disk
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
139667
Show that $f(z) = cg(z)$ is valid for two analytic functions $f$ and $g$ given a certain relationship between them
64172
Show that if $f$ is analytic in a domain $D$ and $|f(z)|$ is constant in $D$, then the function $f(z)$ is constant in $D$
55138
An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$
106175
A function is analytic if and only if it is holomorphic
34542
If $f$ is integrable then $|f|$ is also integrable
23842
$f,\overline f$ are both analytic in a domain $\Omega$ then $f$ is constant?
50342
Proving that a Function is Analytic Given that it is Equal to the Complex Conjugate of an analytic Function
93400
Prove that an analytic function with a constant imaginary part is constant itself
115781
Proof about Holomorphic functions in the unit disc