Let w = 3 + i 2 and P = w^n : n = 1, 2, 3, . Further H_1 = z C : Re z > 1 2 and H_2 = z C : Re z < -1 2 , where C is the set of all complex numbers. If z_1 P H_1, z_2 P H_2 and O represents the origin, then z_1Oz_2 =

JEE Advanced 2013 Mathematics question

Let and . Further and , where is the set of all complex numbers. If , and O represents the origin, then

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

Answer: (C),(D)

Solution

, so P consists of the 12 points on the unit circle. Re z > 1/2 means the argument lies strictly between and : . Re z < −1/2 means the argument lies between and : $

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Question ID VK-026224