Home
Class 12
MATHS
The points z1=0, z2=a-i and z3=1-bi(a,be...

The points `z_1=0, z_2=a-i and z_3=1-bi(a,bepsilon R)` form an equilateral triangle then (A) `a=b=2+sqrt(3)` (B) `a=-b` (C) `a=b=2-sqrt(3)` (D) none of these

A

`a=b=2+sqrt3`

B

`a= b = 2 - sqrt3`

C

`a=b = -2 + sqrt3`

D

`a= b= -2 - sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Similar Questions

Explore conceptually related problems

If a and b are two real number lying between 0 and 1 such that z_1=a+i, z_2=1+bi and z_3=0 form an equilateral triangle , then (A) a=2+sqrt(3) (B) b=4-sqrt(3) (C) a=b=2-sqrt(3) (D) a=2,b=sqrt(3)

If a and b are two real number lying between 0 and 1 such that z_1=a+i, z_2=1+bi and z_3=0 form anequilateral trilangle , then (A) a=2+sqrt(3) (B) b=4-sqrt(3) (C) a=b=2-sqrt(3) (D) a=2,b=sqrt(3)

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 three points (0,\ 0),\ (3,\ sqrt(3)) and (3,\ lambda) form an equilateral triangle, then lambda= (a) 2 (b) -3 (c) -4 (d) None of these

The points A(z_1), B(z_2) and C(z_3) form an isosceles triangle in the Argand plane right angled at B, then (z_1-z_2)/(z_3-z_2) can be (A) 1 (B) -1 (C) -i (D) none of these

If A(1,p^2),B(0,1) and C(p ,0) are the coordinates of three points, then the value of p for which the area of triangle A B C is the minimum is (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) 1/(sqrt(2)) (d) none of these

If z=1/((1-i)(2+3i)), then |z| is (a) . 1 (b ). 1/sqrt(26) (c) . 5/sqrt(26) (d) . none of these

The value of (z + 3) (barz + 3) is equivlent to (A) |z+3|^(2) (B) |z-3| (C) z^2+3 (D) none of these

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=-2,z_3=1-isqrt(3)

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot