Determining whether $f(z)=\ln r + i\theta$ (with domain $\{z:r\gt , 0\lt \theta \lt 2\pi\}$) is analytic
2952
Cauchy-Riemann equations in polar form.
102553
How to show that $f(z) = f(i)$
106175
A function is analytic if and only if it is holomorphic
47474
Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
111056
Harmonic conjugate of $\ln|z|$ in $\mathbb C \setminus \{0\}$
68255
Theorems in complex analysis.
1043
Image of $L=\{z\in\Bbb C \mid a\operatorname{Re}(z)+b\operatorname{Im}(z)+c=0; a^2+b^2\neq0; a,b,c\in \Bbb R \}$ under the function $e^z$
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
158502
Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
125566
The Identity Theorem for real analytic functions
95637
Justifying Calculations on $f(n)=\frac{1}{2 \pi}\int_{-\pi}^{\pi}\theta e^{-in \theta} d \theta$
42075
If $f$ is analytic then $|f|$ is not constant unless $f$ is constant
63446
The existence of analytical branch of the logarithm of a holomorphic function
101900
The analytic function at infinity
111635
Show that if $f(z)$ is a continuous function on a domain $D$ such that $f(z)^N$ is analytic for some integer $N$, then $f(z)$ is analytic on $D$.
23842
$f,\overline f$ are both analytic in a domain $\Omega$ then $f$ is constant?