The pseudo-hyperbolic distance on the unit disk $D$ is defined as: $$\rho(z,w)=\left|\dfrac{z-w}{1-\bar wz}\right|.$$
I need to prove that $(D,\rho(z,w))$ is complete space.
I know that a metric space is called complete if every Cauchy sequence converges, but I really don't know how to prove that this space is complete, could you give me some idea?