If z_1, z_2 are two nonzero complex numbers such that |z_1+z_2| = |z_1| + |z_2| then amp z_1 z_2 is equal to

JEE Advanced Mathematics question

If are two nonzero complex numbers such that then is equal to

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

Answer: (C)

Solution

Equality holds in the triangle inequality only when point in the same direction. That is, are collinear with at one end, so with . Then is a positive real, and

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Question ID VK-108052