If `|z|=1` and let `omega=((1-z)^2)/(1-z^2)` , then prove that the locus of `omega` is equivalent to `|z-2|=|z+2|`

Let z and omega be two complex numbers such that |z|=1 and (omega-1)/(omega+1) = ((z-1)^2)/(z+1)^2 then value of |omega-1| +|omega+1| is equal to____________

What is the locus of w if w=(3)/(z) and |z-1|=1?

If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) = theta . Let omega = (z(1-bar(z)))/(bar(z)(1+z)) , then Re (omega) is equal to

If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1 , find the locus of z in the complex plane

If w=z/[z-1/(3i)] and |w|=1, then find the locus of z

If |z|=1 and |omega-1|=1 where z, omega in C ,then the range of values of |2z-1|^(2)+|2 omega-1|^(2) equals

If z is a complex number satisfying the equation |z-(1+i)|^(2)=2 and omega=(2)/(z), then the locus traced by omega' in the complex plane is

Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then prove that |z|=1.