
Domain of definition
The question
Describe the domain of definition that is understood:
http://latex.codecogs.com/png.latex?...ac{1}{1z^2}
My attempt:
I noticed that http://latex.codecogs.com/png.latex?z^2=z\bar{z} and that http://latex.codecogs.com/png.latex?z=re^{i\theta} in polar form. So,
http://latex.codecogs.com/png.latex?...}=r^2e^{0}=r^2
Thus the denominator becomes 0 if http://latex.codecogs.com/png.latex?r=\pm1, 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.