Let `z_1, z_2, z_3` be three complex numbers and `a ,b ,c` be real numbers not all zero, such that `a+b+c=0` and `a z_1+b z_2+c z_3=0.` Show that `z_1, z_2,z_3` are collinear.

Let z_1, z_2, z_3 be three complex numbers and a ,b ,c be real numbers not all zero, such that a+b+c=0a n da z_1+b z_2+c z_3=0. Show that z_1, z_2,z_3 are collinear.

Let z_(1)z_(2)andz_(3) be three complex numbers and a,b,cin R, such that a+b+c=0andaz_(1)+bz_(2)+cz_(3)=0 then show that z_(1)z_(2)and z_(3) are collinear.

If 2z_1-3z_2 + z_3=0 , then z_1, z_2 and z_3 are represented by

Let z_1, z_2,z_3 be complex numbers (not all real) such that |z_1|=|z_2|=|z_3|=1 and 2(z_1+z_2+z_3)-3z_1 z_2 z_3 is real. Then, Max (arg(z_1), arg(z_2), arg(z_3)) (Given that argument of z_1, z_2, z_3 is possitive ) has minimum value as (kpi)/6 where (k+2) is

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |a b c b c a c a b|=0 a r g(z_3)/(z_2)=a r g((z_3-z_1)/(z_2-z_1))^2 orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 if triangle formed by z_1, z_2, z_3 is equilateral, then 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 _______.

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 where lambda in R-{0}, then prove that points corresponding to z_1, z_2 and z_3 are collinear .

If z_1, z_2, z_3 are three complex, numbers and A=[[a r g z_1,a r g z_3,a r g z_3],[a r g z_2,a r g z_2,a r g z_1],[a r g z_3,a r g z_1,a r g z_2]] Then A divisible by a r g(z_1+z_2+z_3) b. a r g(z_1, z_2, z_3) c. all numbers d. cannot say