GeometryHardQuestion 230016
Question
The complex number z satisfying |z − 2| = |z − 2i| lies on:
- ALine y = xCorrect
- BCircle through origin
- CReal axis
- DImaginary axis
Correct answer
Line y = x
Explanation
Let z = x + iy. |z−2|² = (x−2)² + y². |z−2i|² = x² + (y−2)². Setting equal: (x−2)² + y² = x² + (y−2)² → −4x + 4 = −4y + 4 → x = y. So z lies on y = x.