Home
Class 12
MATHS
If |z1|=|z2|=|z3|=1 then value of |z1-z3...

If `|z_1|=|z_2|=|z_3|=1` then value of `|z_1-z_3|^2+|z_3-z_1|^2+|z_1-z_2|^2` cannot exceed

A

`6`

B

`9`

C

`12`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Let `y=|z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2)`
`=(z_(1)-z_(2))(barz_(1)-barz_(2))+(z_(2)-z_(3))(barz_(2)-barz_(3))+(z_(3)-z_(1))(barz_(3)-barz_(1))`
`=6-(z_(1)barz_(2)+z_(2)barz_(1)+z_(2)barz_(3)+barz_(2)z_(3)+z_(3)barz_(1)+z_(1)barz_(3))`...........`(i)`
Now we know
`|z_(1)+z_(2)+z_(3)|^(2) ge 0`
`implies 3+(z_(1)barz_(2)+z_(2)barz_(1)+z_(1)barz_(3)+z_(3)barz_(1)+z_(2)barz_(3)+barz_(2)z_(3)) ge 0`.........`(ii)`
From `(i)` and `(ii)`, `y le 9`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|16 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|87 Videos

Similar Questions

Explore conceptually related problems

If |z_(1)+z_(2)|=|z_1|+|z_2| then

If |z_1|=|z_2|=|z_3|"…."=|z_n|=1 then |z_(1)+z_(2)+"….."+z_(n)|=

Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

If |z_1-1|lt=1,|z_2-2|lt=2,|z_(3)-3|lt=3, then find the greatest value of |z_1+z_2+z_3|dot

Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1 then prove that |z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|

If a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n z_1+z_2=0 b. z_1z_2=1 c. z_1=z _2 d. none of these

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is

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)