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If z(1) , z(2) are two complex numbers s...

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)|=`

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If z_(1), z_(2) are two non-zero complex numbers satisfying |z_(1)+z_(2)|=|z_(1)|+|z_(2)| , show that Arg z_(1) - Arg z_(2)=0

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Knowledge Check

  • If z_1,z_2 are two complex number satisfying |(z_1-3z_2)/(3-z_1barz_2)|=1, |z_1|ne3, then |z_2|=

    A
    1
    B
    2
    C
    3
    D
    4

  • 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

    A
    Only I is true
    B
    Only II is true
    C
    Both I and II are true
    D
    Neither I nor II are true

  • 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)))|`

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