Home
Class 11
MATHS
P(z1),Q(z2),R(z3)a n dS(z4) are four com...

`P(z_1),Q(z_2),R(z_3)a n dS(z_4)` are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? A)`(z_1-z_4)/(z_2-z_3)` is purely real B) `a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4)` C) `(z_1-z_3)/(z_2-z_4)` is purely imaginary D) It is not necessary that `|z_1-z_3|!=|z_2-z_4|`

Promotional Banner

Similar Questions

Explore conceptually related problems

The points z_(1)z_(2)z_(3)z_(4) in the complex plane are the vertices of a parallelgram taken in order if and only if :

If (2z_1)/(3z_2) is purely imaginary then |(z_(1)-z_(2))/(z_(1)+z_(2))|

z_1, z_2, z_3,z_4 are distinct complex numbers representing the vertices of a quadrilateral A B C D taken in order. If z_1-z_4=z_2-z_3a n d"a r g"[(z_4-z_1)//(z_2-z_1)]=pi//2 , the quadrilateral is a. rectangle b. rhombus c. square d. trapezium

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If z_(1),z_(2)" and "z_(3) are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z_(1),z_(2)" and "z_(3) taken in order 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)

Prove that |z_1+z_2|^2=|z_1|^2+|z_2|^2, ifz_1//z_2 is purely imaginary.

Let the complex numbers z_(1),z_(2),z_(3)" and "z_(4) denote the vertices of a square taken in order. If z_(1)=3+4i" and "z_(3)=5+6i , then the other two vertices z_(2)" and "z_(4) are respectively

The points, z_1,z_2,z_3,z_4, in the complex plane are the vartices of a parallelogram taken in order, if and only if (a) z_1+z_4=z_2+z_3 (b) z_1+z_3=z_2+z_4 (c) z_1+z_2=z_3+z_4 (d) None of these