The locus of the point satisfying is

MATHEMATICS · Single correct · AoPS · Mathematics · Complex Numbers · Complex Numbers

Problem

The locus of the point zz satisfying ∣iz−1∣+∣z−1∣=2|iz-1|+|z-1|=2 is, where i=−1i=\sqrt{-1}, (1) a straight line (2) a circle (3) an ellipse (4) a pair of straight lines

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