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|`

If |z|=1 and omega=(z-1)/(z+1) (where z in -1 ), then Re (omega) is

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?

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|=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

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

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

If arg ((z-omega)/(z-omega^(2)))=0 then prove that Re (z)=-(1)/(2)(omega and omega^(2) are non-real cube roots of unity).