JEE Main 2022 Mathematics question

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and intersect

(1)exactly at one point
(2)exactly at two points
(3)nowhereCorrect
(4)at infinitely many points

Answer: (3)

Solution

The condition means that the segment from −1 to 1 subtends an angle of at z, so z lies on an arc of a circle through (−1, 0) and (1, 0) with centre (0, 1) and

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Question ID VK-035227