JEE Main 2026 Mathematics question
Let the circles C₁ : |z| = r and C₂ : |z − 3 − 4i| = 5, z ∈ ℂ, be such that C₂ lies within C₁. If z₁ moves on C₁, z₂ moves on C₂ and min|z₁ − z₂| = 2, then max|z₁ − z₂| is equal to:
Answer: (C)
Solution
The centre of C₂ is at distance 5 from O. min|z₁ − z₂| = r − 5 − 5 = r − 10 = 2, so r = 12. Then max|z₁ − z₂| = r + 5 + 5 = 22.