What geometric locus is described by |z - 4| = |z + 2i| in the complex plane?
Answer and explanation
Correct answer: C. The perpendicular bisector of the line segment joining (4, 0) and (0, -2)
- Step 1: The condition |z - z_1| = |z - z_2| defines the set of all points equidistant from z_1 and z_2. Step 2. Here z_1 = 4 = (4, 0) and z_2 = -2i = (0, -2). The locus is the perpendicular bisector of the line segment connecting (4, 0) and (0, -2). Answer: The perpendicular bisector of the line segment joining (4, 0) and (0, -2). Why not the others: Points equidistant from two fixed points always trace a straight line bisector.
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