If `z_1, z_2, z_3` are complex numbers such that `(2//z_1)=(1//z_2)+(1//z_3),` then show that the points represented by `z_1, z_2, z_3` lie one a circle passing through the origin.

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2()_, z_3 lie one a circle passing through e origin.

Let z_1 and z_2 be two non - zero complex numbers such that z_1/z_2+z_2/z_1=1 then the origin and points represented by z_1 and z_2

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

If z_1 and z_2 are two complex numbers such that |\z_1|=|\z_2|+|z_1-z_2| show that Im (z_1/z_2)=0

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot

If z_1 is a complex number other than -1 such that |z_1|=1\ a n d\ z_2=(z_1-1)/(z_1+1) , then show that the real parts of z_2 is zero.

If z_1,z_2,z_3 are non zero non collinear complex number such that 2/z_1=1/z_2+ 1/z_3, then (A) ponts z_1,z_2,z_3 form and equilateral triangle (B) points z_1,z_2,z_3 lies on a circle (C) z_1,z_2,z_3 and origin are concylic (D) z_1+z_2+z_3=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 .