Prove that there is no function $f$ that is analytic.
10389
Does there exist an holomorphic function such that $|f(z)|\geq \frac{1}{\sqrt{|z|}}$?
142870
Prove the function is not differentiable at (0,0)
128658
Analyticity of $\overline {f(\bar z)}$ given $f(z)$ is analytic
136714
Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
123249
An analytic function $f$ on $|z|<1$ with $\sup_{|z|<1} |f(z)|=1$ and $|f(0)|=\frac{1}{2}$ has no zeros in $|z|<\frac{1}{2}$
151796
There is not an holomorphic function on a bounded domain such that $\lim_{z \to w} f(z)= \infty$ for every $w \in Fr(\Omega)$
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
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.
46514
Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
27772
Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant.
7861
Non-analytic smooth function
128547
$f:\mathbb C\rightarrow \mathbb C$ be an arbitrary analytic function satisfying $f(0)=0$ and $f(1)=2.$
20955
Let $f(z)$ be analytic on $\mathbb{D}$ = {${z\in\mathbb{C}:|z-1|<1}$} such that $f(1) = 1$, if $f(z) = f(z^2)$ for all $z\in\mathbb{D}$,
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
125566
The Identity Theorem for real analytic functions
68617
Show that an entire function that is real only on the real axis has at most one zero, without the argument principle
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 $D$