Prove that if $f$ is analytic in a region symmetric with respect to the real axis ,then $f (z) = \overline{ f (\bar z)}.$
35378
Prove that $f$ analytic, $f(x) \in \mathbb{R}$ for all $x \in \mathbb{R}$ implies $f(\overline{z})=\overline{f(z)}$
84191
Suppose that $f$ is analytic on a close curve γ. Prove or disprove $\int_\gamma \overline{f(z)}f'(z)dz$ is purely imagine.
3349
For $f$ an analytic function, what is
153411
If $|f|$ is constant, so is $f$ for $f$ analytic on a domain $D$.
115824
Holomorphic functions which preserve orientation
49781
Existence of the absolute value of the limit implies that either $f \ $ or $\bar{f} \ $ is complex-differentiable
65414
One-one analytic functions on unit disc
9844
Proof composition of analytic functions is analytic
112739
The derivative of a holomorphic function on the boundary of the unit circle
74051
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
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 $2013$
125566
The Identity Theorem for real analytic functions
126989
Prove that $g(z)=\overline{f(z)}$ is complex diﬀerentiable at $a$ if and only if $f'(a) = 0$.
19178
$f$ continuous, $f^N$ analytic on a domain D implies $f$ analytic on D
147270
Entire function. Prove that $f(\bar{z})=\overline{f(z)}, \forall z\in C$
47748
Analytic function on an open disc.
64748
analytic in open unit disk,corresponding to a bounded sequence and a bounded functional sequence