Let `|(barz_1-2barz_2)/(2-z_1barz_2)|=1 and |z_2|!=1 where z_1 and z_2` are complex numbers show that `|z_1|=2`

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

Prove that |(z-1)/(1-barz)|=1 where z is as complex number.

If z_1 and z_2 are two complex numbers such that |(barz_1-2barz_2)(2-z_1barz_2)|=1 then (A) |z_1|=1, if |z_2|!=1 (B) |z_1|=2, if |z_2|!=1 (C) |z_2|=2, if |z_1|!=1 (D) |z_2|=1, if |z_1|!=2

(z|barz|^2)/(barz|z|^2) = _______ where z is a complex number of amplitude pi/3 .

Find the complex number z if z^2+barz =0

Prove that |(z_1, z_2)/(1-barz_1z_2)|lt1 if |z_1|lt1,|z_2|lt1