OME 1972 Problem 4

The following sets of points are considered in the plane: $A=\{$ affixes of complexes $z$ such that arg $(z - (2 + 3i))=\pi /4\}$ , $B =\{$ affixes of complexes $z$ such that mod $( z- (2 + i)<2\}$ . Determine the orthogonal projection on the $X$ axis of $A \cap B$ .