For each function describe the domain:

f(z)=Arg(1/z)

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

Thanks

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- Sep 14th 2009, 02:35 PMbethhDomain
For each function describe the domain:

f(z)=Arg(1/z)

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

Thanks - Sep 14th 2009, 03:19 PMpickslides
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Complex Function Grapher - Sep 14th 2009, 04:53 PMredsoxfan325
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 $\displaystyle |z|=1$.