Domain

• September 14th 2009, 02:35 PM
bethh
Domain
For each function describe the domain:

f(z)=Arg(1/z)

f(z)=1/(1-lzl^2)

Thanks
• September 14th 2009, 03:19 PM
pickslides

Complex Function Grapher
• September 14th 2009, 04:53 PM
redsoxfan325
Quote:

Originally Posted by bethh
For each function describe the domain:

f(z)=Arg(1/z)

f(z)=1/(1-lzl^2)

Thanks

The domain will be the entirety of $\mathbb{C}$ except the few points that cause a singularity (i.e. where the denominator will be 0).

For the first one, the domain excludes only $z=0$.

For the second one the domain excludes all points of the form $\cos(\theta) +i\sin(\theta)$, in other words, the unit circle $|z|=1$.