Let `omega=[(z-i)/(1+i z)]^n , n in 1`,then `|omega|=1` all :

Let w=[(z-1)/(1+iz)]^(n),n in I, then |w|=1 for

If z=x+iy and omega=(1-iz)/(z-i) , then |omega|=1 implies that in the complex plane

If z= x + yi and omega = ((1- zi))/(z-i) , then |omega|=1 implies that in the complex plane

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 and omega= (1-zi)/(z-i) show that |omega|=1 rArr z is purely real

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