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

Number of solutions of the equation z^3+[3(barz)^2]/|z|=0 where z is a complex number is

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

if (1+i)z=(1-i)barz then z is

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

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 The value of arg(z_(1)//z_(2)) where z_(1) and z_(2) are complex numbers with the greatest and the least moduli, can be

If |Z-2|=2|Z-1| , then the value of (Re(Z))/(|Z|^(2)) is (where Z is a complex number and Re(Z) represents the real part of 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

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

Prove that there exists no complex number z such that |z| < 1/3 and sum_(n=1)^n a_r z^r =1 , where | a_r|< 2 .