If z_1,z_2 are two complex numbers such that Im (z_1+z_2)=0, Im (z_1z_2)=0, then

JEE Main Mathematics question

If are two complex numbers such that , , then

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

Answer: (C)

Solution

and are both real, so and are roots of a quadratic with real coefficients. Hence they are either both real or a pair of complex conjugates; the non-real case gives , which is the intended relation of option (C)

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Question ID VK-013989