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-3|} , where z is a complex number, 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

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,z_2 be complex numbers with |z_1|=|z_2|=1 prove that |z_1+1| +|z_2+1| +|z_1 z_2+1| geq2 .

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.

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_1+z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2) if |z_1-z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2)=pi