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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
The locus represented by $|z - 1| = |z + i|$ is
  • A
    A circle of radius $1$
  • B
    An ellipse with foci at $(1,\,0)$ and $(0, -1)$
  • ✓
    A straight line through the origin
  • D
    A circle on the line joining $(1,\,0),(0,\,1)$ as diameter
✓

Answer

Correct option: C.
A straight line through the origin
c
(c) $|z - 1|\, = \,|z + i|$ ==> $|x - 1 + iy{|^2} = \,|x + i(y + 1){|^2}$
==> ${(x - 1)^2} + {y^2} = {x^2} + {(y + 1)^2}$
==> $x + y = 0$ i.e., a straight line through the origin.

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