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Question

Let A = {z = C|0 ≤|z-2i| < 1} U {z E C0

(4a) Determine whether A is a connected set or not.

(4b) Find the smallest subset B C A such that A\B is an open set. (we say B is smaller than C if

BCC)

(4c) is the set A\B in the previous part connected?

Fig: 1