Question

The locus of the points representing the complex numbers z for which

|z| – 2 = 0, |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. |z| = 2 represents points on a circle centered at (0, 0) and of radius 2.

i.e., x² + y² = 4 … (1)

|z – i| = |z + 5i| represents points equidistant from the points (0, 1) and (0, –5) i.e.,

x² + (y – 1)² = x² + (y + 5)² Ž y = –2… (2)

Putting y = –2, we get x = 0 from (1). Hence both imply the single point (0, –2).