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, 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 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 nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 w h e r e lambda 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 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 nonzero complex numbers such that z_(3)=(1-lambda)z_(1)+lambda z_(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 are two non zero complex numbers such that z_1/z_2+z_2/z_1=1 then z_1,z_2 and the origin are

z_(1),z_(2),z_(3) and z'_(1),z'_(2),z'_(3) are nonzero complex numbers such that z_(3) = (1-lambda)z_(1) + lambdaz_(2) and z'_(3) = (1-mu)z'_(1) + mu z'_(2) , then which of the following statements is/are ture?

Let Z_(1),Z_(2) be two complex numbers which satisfy |z-i| = 2 and |(z-lambda i)/(z+lambda i)|=1 where lambda in R, then |z_(1)-z_(2)| is