For all complex numbers z_1, z_2 satisfying |z_1| = 12 and |z_2 - 3 - 4i| = 5, the minimum value of |z_1 - z_2| is

JEE Advanced Mathematics question

For all complex numbers satisfying and , the minimum value of is

(A)0
(B)2Correct
(C)7
(D)17

Answer: (B)

Solution

lies on the circle : centre , radius 12; lies on the circle : centre , radius 5. The distance between the centres is , and , so lies entirely inside (it passes through ).

is the dist

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Question ID VK-110585