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 z_(1),z_(2),z_(3) are three complex numbers such that there exists a complex number z with |(:z_(1)-z|=||z_(2)-z|=|backslash z_(3)-z| show that z_(1),z_(2),z_(3) lie on a circle in the Argand diagram.

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

z_1,z_2,z_3 are complex number and p,q,r are real numbers such that: p/(|z_2-z_3|)= q/(|z_3-z_1|)= r/(|z_1-z_2|) . Prove that p^2/(z_2-z_3)= q^2/(z_3-z_1)= r^2/(z_1-z_2)=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 _______.

Let z_(1), z_(2), z_(3) be three non-zero complex numbers such that z_(1) bar(z)_(2) = z_(2) bar(z)_(3) = z_(3) bar(z)_(1) , then z_(1), z_(2), z_(3)

If az_(1)+bz_(2)+cz_(3)=0 for complex numbers z_(1),z_(2),z_(3) and real numbers a,b,c then z_(1),z_(2),z_(3) lie on a