Let S be the set of all complex numbers z satisfying |z-2+i| 5 . If the complex number z_0 is such that 1 |z_0-1| is the maximum of the set 1 |z-1| :z S , then the principal argument of 4-z_0- z_0 z_0- z_0 +2i is

JEE Advanced 2019 Mathematics question

Let be the set of all complex numbers satisfying . If the complex number is such that is the maximum of the set , then the principal argument of is

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

is the region on or outside the circle with centre and radius . is maximum when is minimum. The point lies inside the circle (), so the nearest point of is on the circle along the ray from through :

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Question ID VK-026844