Home
Class 12
MATHS
If z(1),z(2), and z(3) are three complex...

If `z_(1),z_(2), and z_(3)` are three complex numbers such that `|z_(1)| = 1, " " |z_(2)| = 2, " " |z_(3)| = 3 and |z_(1) + z_(2) + z_(3) | = 1,` show that `|9z_(1)z_(2) + 4 z_(1)z_(3) + z_(2)z_(3)| = 6`.

Text Solution

Verified by Experts

The correct Answer is:
6
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.6|5 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.7|6 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.4|7 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    FULL MARKS|Exercise Additional Questions Solved|29 Videos

Similar Questions

Explore conceptually related problems

If z_(1) = 1 - 3i, z_(2) = -4i and z_(3) = 5, show that (z_(1)z_(2)) z_(3) = z_(1) (z_(2)z_(3))

z_(1), z_(3), and z_(3) are complex numbers such that z_(1) + z_(2) + z_(3)=0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 then z_(1)^(2)+z_(2)^(2)+z_(3)^(3)

If z_(1)" and "z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 then

It z_(1) and z_(2) are two complex numbers, such that |z_(1)| = |z_(2)| , then is it necessary that z_(1) = z_(2) ?

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that z_(1)(z_(2) + z_(3)) = z_(1) z_(2) + z_(1) z_(3)

If z_(1) = 3, z_(2) = -7i, and z_(3) = 5 + 4i, show that (z_(1) + z_(2)) z_(3) = z_(1) z_(3) + z_(2) z_(3)