For each function describe the domain:
f(z)=Arg(1/z)
f(z)=1/(1-lzl^2)
Thanks
Check out this link
Complex Function Grapher
The domain will be the entirety of $\displaystyle \mathbb{C}$ except the few points that cause a singularity (i.e. where the denominator will be 0).
For the first one, the domain excludes only $\displaystyle z=0$.
For the second one the domain excludes all points of the form $\displaystyle \cos(\theta) +i\sin(\theta)$, in other words, the unit circle $\displaystyle |z|=1$.