How to tell that 1/(z+2i) is not analytic?

[nutcase21]

hi as shown above, i have come across this expression. But i am not sure how to tell if it is not analytic in the circle |z-2|=4, clockwise.
expression: 1/(z+2i)

On top of that, can anyone give me a general idea of how to see if the expression is analytic or not analytic without using the cauchy's equation.

pls help. thx.

 

[HallsofIvy]

Well, that circle contains the point -2i at which f(x) does not even exist.

 

[nutcase21]

but how do u tell that f(x) does not exist there?

does it mean the function will be come infinite when z=-2i and thus telling us it is not analytic at that point?

 

[chiro]

but how do u tell that f(x) does not exist there?

does it mean the function will be come infinite when z=-2i and thus telling us it is not analytic at that point?

Consider the properties of divergence and also other analytic properties like limits: the limit must be the same from both sides and continuity must hold (among the other properties of analytic functions).