Home
Class 12
MATHS
Let z1,z2,z3 be three complex numbers su...

Let `z_1,z_2,z_3` be three complex numbers such that `|z_1|=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1. Find |9z_1z_2+4z_1z_3+z_2z_3|`.

Answer

Step by step text solution for Let z_1,z_2,z_3 be three complex numbers such that |z_1|=1,|z_2|=2,|z_3|=3 and |z_1+z_2+z_3|=1. Find |9z_1z_2+4z_1z_3+z_2z_3|. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.

If z_1,z_2,z_3 are three complex numbers such that |z_1|=|z_2|=|z_3|=1 , find the maximum value of |z_1-z_2|^2+|z_2-z_3|^2+|z_3+z_1|^2

Knowledge Check

  • Let z_(1), z_(2), z_(3) be three complex numbers such that |z_(1)| = |z_(2)| = |z_(3)| = 1 and z = (z_(1) + z_(2) + z_(3))((1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))) , then |z| cannot exceed

    A
    1
    B
    3
    C
    6
    D
    9
  • If z_1,z_2,z_3 are complex number , such that |z_1|=2, |z_2|=3, |z_3|=4 , the maximum value |z_1-z_2|^(2) + |z_2-z_3|^2 + |z_3-z_1|^2 is :

    A
    58
    B
    29
    C
    87
    D
    None of these
  • If z_1 , z_2, z_3 are complex numbers such that |z_1|= |z_2| = |z_3|= |(1)/(z_1) + (1)/(z_2) + (1)/(z_3)|=1, then [ (1+ i)^(n_1) + (1-i)^(n_1)] + [ (1+ i)^(n_2) + (1-i)^(n_2)] is

    A
    equal to 1
    B
    less than one
    C
    greater than 3
    D
    equal to 3
  • Similar Questions

    Explore conceptually related problems

    Let z_(1)z_(2),z_(3), be three complex number such that z_(1)+z_(2)+z_(3)=0 and |z_(1)|=|z_(2)|=|z_(3)|=1 then Let |z_(1)^(2)+2z_(2)^(2)+z_(3)^(2)| equals

    Given the z_(1),z_(2) and z_(3) are complex numbers with |z_(1)|=1,|z_(2)|=1,|z_(3)|=1, and z_(1)+z_(2)+z_(3)=1 and z_(1)z_(2)z_(3)=1 find |(z_(1)+2)(z_(2)+2)(z_(3)+2)|

    If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

    If z_1,z_2 are complex numbers such that, |(z_1-3z_2)/(3-z_1.bar z_2)|=1 and |z_2|ne 1 then find |z_1|

    Let z_(1),z_(2),z_(3) be complex numbers (not all real) such that |z_(1)|=|z_(2)|=|z_(3)|=1 and 2(z_(1)+z_(2)+z_(3))-3z_(1)z_(2)z_(3) is real.Then,Max(arg(z_(1)),arg(z_(2)),arg(z_(3))) (Given that argument of z_(1),z_(2),z_(3) is possitive ) has minimum value as (k pi)/(6) where (k+2) is