Home
Class 12
MATHS
Assertion (A): z1,z2 and origin form an ...

Assertion (A): `z_1,z_2 and` origin form an equilateral triangle if `p^2=6q` for the equation `z^2 + pz+q=0`, Reason (R): Triangle having vertices `z_1,z_2,z_3` in the Argand plane is equilateral if `z_1^2+z_2^2+z_3^2=z_1z_2+z_2z_3+z3z_1` (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

Assertion (A): z/(4-z^2) lies on y-axis. Reason (R): |z|^2= zbarz (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not te correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion (A): argz_1-argz_2=0 , Reason: If |z_1+z_2|=|z_1|+|z_2| , then origin z_1,z_2 are colinear and z_1,z_2 lie on the same side of the origin. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Assertion (A): Circumcentre of /_\POQ is (z_1+z_2)/2 , Reason (R): Circumcentre of a right triangle is the middle point of the hypotenuse. (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If alpha, beta are complex numbers, then maximum value of (alphabarbeta+ baralpha beta)/(|alphabeta|) is 2. Reason (R): For any two complex numbers z_1 and z_2, |z_1-z_2|ge|z_1|-|z_2| (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

The complex numbers z_1, z_2 and the origin form an equilateral triangle only if (A) z_1^2+z_2^2-z_1z_2=0 (B) z_1+z_2=z_1z_2 (C) z_1^2-z_2^2=z_1z_2 (D) none of these

If z_0 is the circumcenter of an equilateral triangle with vertices z_1, z_2, z_3 then z_1^2+z_2^2+z_3^2 is equal to

lf z_1,z_2,z_3 are vertices of an equilateral triangle inscribed in the circle |z| = 2 and if z_1 = 1 + iotasqrt3 , then

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

Prove that traingle by complex numbers z_(1),z_(2) and z_(3) is equilateral if |z_(1)|=|z_(2)| = |z_(3)| and z_(1) + z_(2) + z_(3)=0

if the complex no z_1 , z_2 and z_3 represents the vertices of an equilateral triangle such that |z_1| = | z_2| = | z_3| then relation among z_1 , z_2 and z_3