Where are these functions analytic?

[Damascus Road]

Greetings all, I have 2 functions:

$$\frac{1}{Rez} + \frac{1}{Imz}(z^{2}- \overline{z}^{2})$$

and

$$\frac{1}{Rez} + \frac{1}{i Imz}(z^{2}- \overline{z}^{2})$$

I have to find where they are analytic, how do I start this?

 

[gabbagabbahey]

A good place to start is to look up the definition of analytic

You may also want to look up "Cauchy-Riemann equations". They provide a simple test for the analyticity of a function.