Verified Solution • 2025–26 Session moderate

QJEEM19Ma18cd: JEE Main 2019 Mathematics - Class 11 JEEM19Ma18cd Solution: Let z 1 and z 2 be two complex numbers satisfying

Let z1 and z2 be two complex numbers satisfying | z1 | = 9 and | z2 – 3 – 4i | = 4. Then the minimum value of | z1 – z2 | is :

Multiple Choice Options

  • A 0
  • B 1
  • C 2
  • D 2\sqrt 2

Step-by-Step Verified Solution

∣z1∣=9,  ∣z2−(3+4i)∣=4\left| {{z_1}} \right| = 9,\,\,\left| {{z_2} - \left( {3 + 4i} \right)} \right| = 4

C1,(0,0){C_1},(0,0) radius r1 = 9

C2 (3, 4), radius r2 = 4

C1C2 = ∣r1−r2∣=5\left| {{r_1} - {r_2}} \right| = 5

∴\therefore   Circle touches internally

∴\therefore    ∣z1−z2∣min⁡=0{\left| {{z_1} - {z_2}} \right|_{\min }} = 0

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