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.

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

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 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^(2) + z + 1 = 0 where z is a complex num ber, then (z+(1)/(z))^(2)+(z^(2)+(1)/(z^(2)))^(2)+(z^(3)+(1)/(z^(3)))^(2) equal

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) - 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.