Thread: Domain of definition

The question

Describe the domain of definition that is understood:



My attempt:
I noticed that and that in polar form. So,



Thus the denominator becomes 0 if , so there is no domain at these points. Is this correct? Any assistance would be truly appreciated!

|z|^2 is a real number, so 1/(1 - |z|^2) is also a real number. For what values will this real number be defined?

When (1 - |z|^2) != 0

Or, x^2 + y^2 != 1

Correct.

So the domain is all z such that |z| =/= 1.