Multiple Choice Questions on Let z1 z2 and z3 be non zero complex numbers satisfying z2 i 2 where i........... for NDA Exam Preparation

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Multiple Choice Questions

Let z1 z2 and z3 be non zero complex numbers satisfying z2 i 2 where i...........

Mathematics (NDA) Complex Numbers
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    Let z1, z2 and z3 be non-zero complex numbers satisfying z2 = i \small \bar{z},  2 = ,where i = \small \sqrt{-1}.

    Consider the following statements

    1. z1z 2z 3 is purely imaginary.

    2. z1z2 +z 2z 3 + z 3z1  is purely real.

    Which of the above statements is/are correct?

    Only 1

    Incorrect Answer

    Only 2

    Incorrect Answer

    Both 1 and 2 

    Correct Answer

    Neither 1 nor 2

    Incorrect Answer
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    Explanation:

    We have, z1z2 z3 = i  
    =>  z1 z2 z3  is purely imaginary.
    Statement 1 is correct and z1 z2 +z2 z3 + z3 z1 = 0
    =>  z1 z2 +z2 z3 + z3 z1 is purely real.
    Statement 2 is correct.

    By: Munesh Kumari
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