We have,
C1:∣z1∣=9
C2:∣z2−3−4i∣=4
Centres of the circles are c1≡(0,0) and c2≡(3,4).
Radius of the circles are r1=9 and r2=4.
⇒c1c2=32+42=5 and r1−r2=5
Circles touch each other internally.
⇒∣z1−z2∣min=0 at the point of contact.
Let z1 and z2 be two complex numbers satisfying ∣z1∣=9 and ∣z2−3−4i∣=4. Then the minimum value of ∣z1−z2∣ is :
Held on 12 Jan 2019 · Verified 6 Jul 2026.
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