The complex numbers `z_1, z_2 and z_3` satisfying `(z_1-z_3)/(z_2-z_3) =(1- i sqrt(3))/2` are the vertices of triangle which is (1) of area zero (2) right angled isosceles(3) equilateral (4) obtuse angled isosceles

The complex numbers z_(1),z_(2),z_(3) stisfying (z_(2)-z_(3))=(1+i)(z_(1)-z_(3)).where i=sqrt(-1), are vertices of a triangle which is

The complex numbers z 1 ​ ,z 2 ​ and z 3 ​ satisfying z 2 ​ −z 3 ​ z 1 ​ −z 3 ​ ​ = 2 1− 3 ​ i ​ are the vertices of a triangle which is

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

The complex numbers z_1=1+2i,z_2=4-2i and z_3=1-6i form the vertices of a (A) a right angled triangle (B) isosceles triangle (C) equilateral triangle (D) triangle whose one of the sides is of length 8

For any complex numbers z_1,z_2 and z_3, z_3 Im(bar(z_2)z_3) +z_2Im(bar(z_3)z_1) + z_1 Im(bar(z_1)z_2) is

If z_(1)=1+2i, z_(2)=2+3i, z_(3)=3+4i , then z_(1),z_(2) and z_(3) represent the vertices of a/an.

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 , find the minimum value of |z_1-z_2|

If the complex numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

Let z_1 , z _2 and z_3 be three complex numbers such that z_1 + z_2+ z_3 = z_1z_2 + z_2z_3 + z_1 z_3 = z_1 z_2z_3 = 1 . Then the area of triangle formed by points A(z_1 ), B(z_2) and C(z_3) in complex plane is _______.