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

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

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

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

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

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 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 z=x+iy and w=(1-iz)/(z-i) , then |w|=1 implies that in the complex plane (A) z lies on imaginary axis (B) z lies on real axis (C) z lies on unit circle (D) None of these

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

If complex number z lies on the curve |z - (- 1+ i)| = 1 , then find the locus of the complex number w =(z+i)/(1-i), i =sqrt-1 .

If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of the point representing in the complex plane.