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.`

Let |(z_(1) - 2z_(2))//(2-z_(1)z_(2))|= 1 and |z_(2)| ne 1 , where z_(1) and z_(2) are complex numbers. shown that |z_(1)| = 2

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

Complex numbers z satisfy the equaiton |z-(4//z)|=2 Locus of z if |z-z_(1)| = |z-z_(2)| , where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, is

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , 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

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

If z be a non-zero complex number, show that (bar(z^(-1)))= (bar(z))^(-1)

For any two complex number z_1a n d\ z_2 prove that: |z_1-z_2|lt=|z_1|+|z_2|

If z_1 and z_2 are two complex numbers such that (z_1-2z_2)/(2-z_1bar(z_2)) is unimodular whereas z_1 is not unimodular then |z_1| =

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 .