Show that $\log(x^2+y^2)$ is not a real part of analytic function in $z\ne 0$.
39583
ii) Show that $u$ is not a real part of the function which analytic on $\mathbb{C} \backslash \lbrace 0 \rbrace$
77464
Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
141863
If the imaginary part of an entire function is never zero, the function is constant
111760
If $f^2$ is an analytic function then so is $f$
99726
Proving that a function is not a contraction
69090
The family of analytic functions with positive real part is normal
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 $D$
141254
Zeros of analytic function of several real variables
127605
What are some methods to show $\log$ is not a rational function?
153855
Complex analysis, showing a function is constant
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
138559
How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$?
125701
Prove that $-2\log(2) = -2 + \sum_{n=1}^{\infty}\frac{1}{n(2n+1)}$
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
48619
Let $f$ be a non-constant analytic function on $\mathbb{D}$ satisfying $|f(z^2)| ≤ |f(z)|$ for $|z| < 1.$
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$