Show that $d(z,w)=\lvert \frac{z-w}{1-\overline{w}z}\rvert$ is a metric function on the unit disk
112329
Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
120985
Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
112739
The derivative of a holomorphic function on the boundary of the unit circle
35291
How to show $d(x,y)= \sqrt{d_1(x_1,y_1)^2+d_2(x_2,y_2)^2}$ is a metric?
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
57816
$(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$
102553
How to show that $f(z) = f(i)$
98660
(complex measures) $d\nu=d\lambda +f\,dm \Rightarrow d|\nu|=d|\lambda| +|f|\,dm$ and $f\in L^1(\nu)\Rightarrow f\in L^1(|\nu|)$
128658
Analyticity of $\overline {f(\bar z)}$ given $f(z)$ is analytic
108779
How to prove that this series is a metric: $d(x,y):=\sum_{i=0}^\infty \frac{|x_i -y_i|}{2^i (1+|x_i-y_i|)}$
127169
Show that the zeros of $\sum_{k=1}^n kz^{k-1}$ are inside the unit disc
141643
Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
157296
Homeomorphism between the Unit Disc and Complex Plane
123039
If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
150689
All the zeroes of $p(z)$ lie inside the unit disk
132657
Function $ f $ defined on unit disk $ D $ has real values on $ \partial D $, why is $ f $ real valued?
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric