Home
Class 12
MATHS
If z(1),z(2) and z(3) be unimodular comp...

If `z_(1),z_(2)` and `z_(3)` be unimodular complex numbers, then the maximum value of `|z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2)`, is

A

6

B

9

C

12

D

none

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (1) (True and False)|5 Videos
  • COMPLEX NUMBERS

    ML KHANNA|Exercise Problem Set (2) (M.C.Q)|111 Videos
  • CO-ORDINATE GEOMETRY OF THREE DIMENSION

    ML KHANNA|Exercise SELF ASSIGNMENT TEST |11 Videos
  • CONCEPTS OF SET THEORY

    ML KHANNA|Exercise Self Assessment Test|13 Videos

Similar Questions

Explore conceptually related problems

For any two complex numbers z_(1),z_(2) the values of |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) , is

If Z_(1),Z_(2) are two non-zero complex numbers, then the maximum value of (Z_(1)bar(Z)_(2)+Z_(2)bar(Z)_(1))/(2|Z_(1)||Z_(2)|) is

If z_(1) and z_(2) are unimodular complex numbers that satisfy z_(1)^(2)+z_(2)^(2)=4, then (z_(1)+bar(z)_(1))^(2)+(z_(2)+bar(z)_(2))^(2) equals to

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

If z_(1),z_(2) and z_(3),z_(4) are two pairs of conjugate complex numbers,hen find the value of arg(z_(1)/z_(4))+arg(z_(2)/z_(3))*a

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 :

Match the following : {:("Column-I" ," Column-II"),("(A) The value of " underset(k=1)overset(2007)sum (sin""(2kpi)/9 - icos""(2kpi)/9) " is" , " (p) -1"),("(B) If " z_(1)","z_(2) and z_(3) " are unimodular complex numbers such that " |z_(1)+z_(2)+z_(3)|=1 " then " |1/z_(1)+1/z_(2) + 1/z_(3)| " is equal to " , " (q) 2 "),("(C) If the complex numbers " z_(1)"," z_(2) and z_(3) " represent the vetices of an equilateral triangle such that " |z_(1)|=|z_(2)|=|z_(3)| " then " (z_(1) +z_(2) +z_(3)) -1 " is equal to " , " (r) 1"),("(D) If " alpha " is an imaginary fifth root of unity , then " 4log_(4)| 1+alpha +alpha^(2) +alpha^(3) -1/alpha| " is " , " (s) 0"):}

If z_(1),z_(2),z_(3) are distinct nonzero complex numbers and a,b,c in R^(+) such that (a)/(|z_(1)-z_(2)|)=(b)/(|z_(2)-z_(3)|)=(c)/(|z_(3)-z_(1)|) Then find the value of (a^(2))/(z_(1)-z_(2))+(b^(2))/(z_(2)-z_(3))+(c^(2))/(z_(3)-z_(1))

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)