Home
Class 12
MATHS
If the complex numbers z(1) , z(2) , z(3...

If the complex numbers `z_(1) , z_(2) , z_(3)` represents the vertices of an equilateral triangle such that `|z_1| = |z_2| = |z_3|` then

A

`z_(1) + z_(2) = z_(3)`

B

`z_(1) + z_(3) = z_(2)`

C

`z_(2) + z_(3) = z_(1)`

D

`z_(1) + z_(2) + z_(3) = 0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise EXERCISE -II|126 Videos

  • CIRCLES

    AAKASH SERIES|Exercise PRACTICE EXERCISE|164 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

Similar Questions

Explore conceptually related problems

Let the complex number z_(1) , z_(2) , z_(3) be the vertices of an equilateral triangle . Let z_(theta) be the circumcentre of the triangle . Then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) =

If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)

Let the complex number z_1,z_2,z_3 be the vertices of an equilateral triangle . Let z_0 be the circumcentre of the triangle . Then z_1^2+z_2^2+z_3^2=

Assertion (A) : The origin and the roots of the equation x^(2) + ax + b = 0 form an equilateral triangle if a^(2) = 3b Reason (R) : If z_(1) , z_(2) , z_(3) are vertices of an equilateral triangle then z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = z_(1) z_(2) + z_(2) z_(3) + z_(3) z_(1)

If z_1,z_2,z_3 are the vertices of a triangle then its centroid is

If (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_3), z_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2)=(x_(3)-2)^(3)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sumy_(1)+3sum z_(1)=

If the complex number z lies on |z| = 1 then (2)/(z) lies on

The complex number z satisfying z^(2) + |z| = 0 is

If z_1=1+2i,z_2=2+3i,z_3=3+4i, " then " z_1,z_2and z_3 represents the vertices of