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Locus in complex plane

Source: Czech and Slovak Olympiad 1977, National Round, Problem 3

October 10, 2024
geometrycomplex numbersLocus

Problem Statement

Consider any complex units Z,WZ,W with Im Z≥0,Re W≥0.\text{Im}\ Z\ge0,\text{Re}\,W\ge 0. Determine and draw the locus of all possible sums S=Z+WS=Z+W in the complex plane.
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