Statement 1: If z_1 and z_2 are two complex numbers such that |z_1|=|z_2|+|z_1-z_2|, then Im ( z_1 z_2 )=0 Statement 2: (z)=0 z is purely real

JEE Main Mathematics question

Statement 1: If and are two complex numbers such that , then Statement 2: is purely real

(A)Assertion is True, Reason is True; Reason is correct explanation for AssertionCorrect
(B)Assertion is True, Reason is True; Reason is not correct explanation for Assertion
(C)Assertion is True, Reason is False
(D)Assertion is False, Reason is True

Answer: (A)

is the equality case of the triangle inequality , so lies on the segment from to and is a positive real number, whose argument is

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Question ID VK-013588