True or false? Justify.

Let be an isolated singularity of f(z) such that . Then is a removable singularity and thus is analytic in a neighborhood of .

Attempt: True. I know that if is a removable singularity, then f can be extended to an analytic function by giving a value to . Thus I also believe that f is bounded if its singularity is removable.

Though formally I don't know how to prove it. If (I know I assume that f has a Laurent series representation, I'm not sure I can assume that) then I'm told that . I'm not going far with this.

Any idea?