Let `|(( bar z _1)-2( bar z _2))//(2-z_1( bar z _2))|=1` and `|z_2|!=1`,where `z_1` and `z_2` are complex numbers. Show that `|z_1|=2.`

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If |z_(1)|=|z_(2)|and argz_(1)+argz_(2)=0, then show that z_(1) and z_(2) are tow complex conjugate numbers. '

If z_(1)and z_(2) are conjugate complex number, then z_(1)+z_(2) will be

If z_(1)+z_(2) are two complex number and |(barz_(1)-2bar z_(2))/(2-z_(1)barz_(2))|=1, |z_(1)| ne , then show that |z_(1)|=2 .

If z_(1),z_(2) are two complex numbers , prove that , |z_(1)+z_(2)|le|z_(1)|+|z_(2)|

A complex number z is said to be unimodular if absz=1 suppose z_1 and z_2 are complex numbers such that ( z_1-2z_2)/(2-z_1z_2) is unimodular and z_2 in not unimodular then the point z_1 lies on a

Let A(z_1) and (z_2) represent two complex numbers on the complex plane. Suppose the complex slope of the line joining A and B is defined as (z_1-z_2)/(bar z_1-bar z_2) .If the line l_1 , with complex slope omega_1, and l_2 , with complex slope omeg_2 , on the complex plane are perpendicular then prove that omega_1+omega_2=0 .

If z_1 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

A complex number z is said to be unimodular if |z|=1 Suppose z_(1)andz_(2) are complex number such that (z_(1)-^(2z)2)/(2-z_(1)z_2) is unimodular and z_(2) is not unimodular .Then the point z_(1) lies on a -

If z_(1)^(2)+z_(2)^(2)+z_(3)^(2)-z_(1)z_(3)-z_(1)z_(2)-z_(2)z_(3)=0" ""prove that" " "|z_(2)-z_(3)|=|z_(3)-z_(1)|=|z_(1)-z_(2)|, "where" " " z_(1),z_(2),z_(3) are complex numbers.