What Are the Domains of Definition for These Complex Functions?

[DEMJ]

Homework Statement

Describe the domain of definition that is understood for each of the functions:

(a) $$f(z) = \frac{1}{1 - |z|^2}$$

(b) $$f(z) = \frac{z}{z + \bar{z}}$$

(c) $$f(z) = Arg(\frac{1}{z})$$

(d) $$f(z) = \frac{1}{z^2+1}$$

Homework Equations

A function f defined on S is a rule that assigns to each z in S a complex number w. The number w is called the value of f at z and is denoted by f(z); that is w = f(z). The set S is called the domain of definition of f.

The Attempt at a Solution

I really do not know how I should approach the problem. Since it is an odd problem the book has only this listed as answers (b) $$Rez \not= 0$$ (d) $$z \not= \pm i$$

I understand that for (b) and (d) that these values will make the denominator = 0. What I do not understand is what I should be describing in (a) and (c). Is it really that simple of a question where you just describe only where the functions are undefined? Anyone care give me any suggestions on where to even start thinking? because I am really struggling on this problem that should be easy since it's the first one of the 2nd chapter.

 

[LCKurtz]

Yes, it is that easy.