How to show that log|z| has no harmonic conjugate on the complex plane with origin removed?
111056
Harmonic conjugate of $\ln|z|$ in $\mathbb C \setminus \{0\}$
2348
Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
57677
Decomposition of Harmonic function into sum of holomorphic and anti-holomorphic function
14447
Direct proof that $\pi$ is not constructible
63446
The existence of analytical branch of the logarithm of a holomorphic function
27933
Show that unit circle is not homeomorphic to the real line
52864
Line integration in complex analysis
88474
$\mathbb{A}^{2}$ not isomorphic to affine space minus the origin
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
12401
Is it standard to say $-i \log(-1)$ is $\pi$?
112060
Is complex conjugation needed for valid inner product?
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
89380
A positive harmonic function on the punctured plane is constant
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
107450
False proof that $ρe^{iθ} = ρ$ and so complex numbers do not exist?
74051
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
23801
A reflection question about a complex function