Complex Numbers
Locus and Geometry
JEE Advanced 2010
Grade 11

Question:

The number of complex numbers $z$ satisfying $|z - 1| = |z + 1| = |z - i|$ is:
(1) $0$
(2) $1$
(3) $2$
(4) $3$

Step-by-Step Solution

Key Concept: Each equality is a perpendicular bisector condition. $|z - 1| = |z + 1|$ gives $\operatorname{Re}(z) = 0$; find the second condition and take the intersection.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)

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