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For any two complex numbers z(1) and z(2...

For any two complex numbers `z_(1)` and `z_(2)`, prove that Re (`z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)`

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Knowledge Check

  • For any two complex numbers z_(1) & z_(2) and any two real numbers a , b |az_(1) - bz_(2)|^(2) + |bz_(1) + az_(2)|^(2) =

    A
    `(a^(2) - b^(2)) (|z_(1)|^(2) + |z_(2)|^(2))`
    B
    `(a^(2) + b^(2)) (|z_(1)|^(2) + |z_(2)|^(2))`
    C
    `(a^(2) + b^(2)) (|z_(1)|^(2) - |z_(2)|^(2))`
    D
    `(a^(2) -b^(2)) (| z_(1)|^(2) - |z_(2)|^(2))`

  • If z_(1) , z_(2) are two complex numbers satisfying |(z_(1) - 3z_(2))/(3 - z_(1) barz_(2))| = 1 , |z_(1)| ne 3 then |z_(2)|=

    A
    1
    B
    2
    C
    3
    D
    4

  • If |z_(1) | = |z_(2)| = 1 , then |z_(1) + z_(2)| =

    A
    `|(1)/(z_(1)) + (1)/(z_(2))|`
    B
    `| (1)/(z_(1)) - (1)/(z_(2))|`
    C
    `| (1)/(z_(1)) * (1)/(z_(2))|`
    D
    `| (1)/(z_(1)^(2)) + (1)/(z_(2)^(2)))|`

    • Similar Questions

    Explore conceptually related problems

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    Statement - I : If z_(1) and z_(2) are two nonzero complex numbers such that |z_(1) + z_(2) | = |z_(1)| + |z_(2)| then arg z_(1) - arg z_(2) is pi//2 Statement - II : z_(1) and z_(2) are two complex numbers such that |z_(1) z_(2)| = 1 and arg z_(1) - arg z_(2) is pi//2 then barz_(1) z_(2) = -i

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