If there exists an Z satisfying both |Z –mi| = m + 5 and |Z…

Maths Complex Number The Modulus and the Conjugate of a Complex Number Single Correct MCQ

Published on: August 13, 2026

If there exists an Z satisfying both |Z –mi| = m + 5 and |Z–4| < 3, then the set of all permissible values of m belong to the set -

(–3, 3)

(–3, 9)

(–5, –3)

(4, 9)

Text Solution

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The correct answer is:

|Z –mi| = m + 5 represents a circle with mi or B(0, m) as centre and radius m + 5.

|Z –4| < 3 represents the interior of a circle with centre 4 or A(4, 0) and radius 3.

If there is to be at least one Z satisfying both the two circles should intersect.

(i.e.) r 1 ~ r 2 < d < r 1 + r 2

m + 5 – 3 < < m + 5 + 3

squaring, m 2 + 4m + 4 < m 2 + 16 < m 2 + 16 m + 64

∴ m < 3 and m > –3

∴ m (–3, 3)

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