Given $f(z)$ is an analytic complex function, show $f^*(z^*)$ is also analytic
12525
complex conjugates of holomorphic functions
84301
Showing that some Function on the Unit Disc is injective
137718
Prove that the complex expression is real
74051
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
34719
Show this holomorphic function is constant
6722
to show $f$ is a polynomial in $z$
69020
Complex analysis : If $z =re^{i\theta}$, then prove that $|e^{iz}| =e^{-r\sin\theta}$
11062
$f(z)=\frac1{2\pi i}\int_{\Gamma}\frac{f(\zeta)}{z-\zeta}d\zeta$ if $\lim_{z\to\infty}f(z)=0$ and $f$ is analytic in $|z|\ge1$
102553
How to show that $f(z) = f(i)$
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
132907
The inverse of a bijective holomorphic function is also holomorphic
148474
on the boundary of analytic functions
65901
Solution verification to complex analysis problem, prove $f$ is a polynomial.
70361
if a complex function $f$ is real-differentiable, then $f$ or $\overline{f}$ are complex-differentiable
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
116092
Non constant analytic function from $\{z\in\mathbb{C}:z\neq 0\}$ to $\{z\in\mathbb{C}:|z|>1\}.$
96547
Is $|z|^2$ complex differentiable?