If `z_1, z_2, z_3` are three nonzero complex numbers such that `z_3=(1-lambda)z_1+lambdaz_2w h e r elambda in R-{0},` then prove that points corresponding to `z_1, z_2a n dz_3` are collinear .

If z_(1),z_(2),z_(3) are three non-zero complex numbers such that z_(3)=(1-lambda)z_(1)+lambda z_(2) where lambda in R-{0}, then points corresponding to z_(1),z_(2) and z_(3) is

If z_1 and z_2 are two nonzero complex numbers such that |z_1-z_2|=|z_1|-|z_2| then arg z_1 -arg z_2 is equal to

If z_1,z_2 are nonzero complex numbers then |(z_1)/(|z_1|)+(z_2)/(|z_2|)|le2 .

Let z_1, z_2, z_3 be three distinct complex numbers satisfying |z_1 - 1| = |z_2-1| = |z_3-1| . Let A , B, and C be the points represented in the Argand plane corresponding to z_1 , z_2 and z_3 respectively. Prove that z_1 + z_2 + z_3=3 if and only if Delta ABC is an equilateral triangle.

If |2z-1|=|z-2| and z_(1),z_(2),z_(3) are complex numbers such that |z_(1)-alpha| |z|d.>2|z|

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)