Let z be a complex number satisfying |z-5i| 1 such that amp (z) is minimum. Then z is equal to

JEE Main Mathematics question

Let be a complex number satisfying such that is minimum. Then is equal to

(A)Correct
(B)
(C)
(D)None of these

Answer: (A)

Solution

The region is the disc of radius centred at ; the least argument occurs at the tangent from the origin on the right side. The tangent length is and the angle with the imaginary axis

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Question ID VK-013637