If z=x+iy and w=(1-iz)/(z-i), then |w|=...

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

Similar Questions

Explore conceptually related problems

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

The point z in the complex plane satisfying |z+2|-|z-2|= ±3 lies on

If |z+barz|+|z-barz|=2 then z lies on (a) a straight line (b) a set of four lines (c) a circle (d) None of these

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

The complex number z which satisfies the condition |(i+z)/(i-z)| = 1 lies on

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

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

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|