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

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

The system of equations |z+1-i|=2 and Re(z)>=1 where z is a complex number has

The number of solutions of the equation z^(3)+(3(barz)^(2))/(|z|)=0 (where, z is a complex number) are

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

If f(z) = a_0z^n+a_1z^(n-1)+a_2z^(n-2)+...+a_n where z is a complex number and a_1 , a_2 , etc , are real , prove that barf(z)=f(barz) .

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

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

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 |Z-i|=sqrt(2) then arg((Z-1)/(Z+1)) is (where i=sqrt(-1)) ; Z is a complex number )