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projections on sets on complex plane

Source: Spanish Mathematical Olympiad 1972 P4

December 5, 2022
complex numbers

Problem Statement

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