If z is a complex number in the Argand plane such that ( z-3 3 z+3 3 )= 3, then the locus of z is

JEE Main Mathematics question

If is a complex number in the Argand plane such that , then the locus of is

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

Answer: (B)

Solution

The segment joining and has length and subtends the constant angle at , so lies on a circle of radius whose centre is on the imaginary axis at . For with ,

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Question ID VK-013999