If `|2z-1|=|z-2|` prove that `|z|=1` where z is a complex

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

If |z-2|=min{|z-1|,|z-5|}, where z is a complex number then

If |z-2|= "min" {|z-1|,|z-3|} , where z is a complex number, then

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

If |2z-1|=|z-2| and z_(1),z_(2),z_(3) are complex numbers such that |z_(1)-alpha| |z|d.>2|z|

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

Let z_1, z_2 be two complex numbers with |z_1| = |z_2| . Prove that ((z_1 + z_2)^2)/(z_1 z_2) is real.

If |(z-z_1)/(z-z_2)|=1 , where z_1 and z_2 are fixed complex numbers and z is a variable complex number, then z lies on a