" 1.Let "z=x+iy" and "omega=(1-iz)/(z-i)" .If "| omega|=1," show that "z" is purely real."

If z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is purely real.

If z=x+iyandw=(1-iz)/(z-i) such that |w|=1 , then show that z is purely real.

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

If z=x+iy and w=(1-iz)/(1+iz) such that |w|=1.then show that z is purely real.

Let z=x+iy and omega=(1-iz)/(z-i). If |omega|=1 show the in the complex plane the point z lies on the real axis.

If z=x+i y and w=(1-i z)/(z-i) , show that |w|=1 z is purely real.

If omega=(z)/(z-(1/3)i)" and "|omega|=1 , then z lies on

If z = x + iy and w=(1-iz)/(z-i) , show that : |w|=1 implies z is purely real.

Suppose z = x + iy and w = (1-iz)/(z-i) Find absw . If absw = 1, prove that z is purely real

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