Question

The locus of the points representing the complex numbers z for which |z| – 2 = |z – i| – |z + 5i| = 0 is –

• A. A circle with centre at origin
• B. A straight line passing through origin
• C. The single point (0, –2)
• D. None of these

Answer 1

Answer: (C)

The single point (0, –2)

Answer 2

Sol. We have |z| – 2 = |z – i| – |z + 5i| = 0 … (1)

(1) Ž |z| – 2 = 0 Ž |z| = 2 … (2)

(1) Ž |z – i| = |z + 5i| … (3)

(1) Represents the circle with centre at origin and radius 2

(2) Represents the perpendicular bisector of the line segment joining A (0, 1) and B(0, –5).

For y = –2, the point P(0, –2) lies on the circle.

\ The locus is the single point (0, –2).