Question

For all complex numbers z₁,z₂, satisfying |z| = 12 and |z - 3 - 4i| = 5 the minimum value of |z₁ - z₂|  is 

(1) 0 

(2) 2 

(3) 7 

(4) 17

Answer 1

Correct option is (2) 2

Explanation:

circle |z| = 12 centre c₁(0, 0), radius r₁ = 12.

circle |z - 3 -4i| = 5 centre c₂ (3, 4), radius r₂ = 5 

OP = 5 <7 =r₁. r₂

Hence circle 1st lies inside 2nd circle 

Therefore minimum distance between them is AB = c₁ B- c₁ A=12-10=2