The equation |z + 1 - i| = |z - 1 + i| represents a (where z is a complex number)

MHT CET 2025 Mathematics question

The equation represents a (where z is a complex number)

(A)Straight line passing through the origin and the first and third quadrantCorrect
(B)Straight line passing through the origin and the second and fourth quadrant
(C)Straight line passing through the point (1, -1) and having slope -1
(D)Straight line passing through the point (2, 1) and having slope

Answer: (A)

Solution

says that is equidistant from (the point ) and (the point ), so lies on the perpendicular bisector of these points. Algebraically, with : , which gives , i.e. $y =

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Question ID VK-101383