$z=x+iy$ and $\omega=\large\frac{1-iz}{z-i}$ then $|\omega|=1$ implies that in complex plane

Question

$\begin{array}{1 1}(A)\;\text{z lies on real axis}\\(B)\;\text{z lies on imaginary axis}\\(C)\;\text{z lies on a unit circle}\\(D)\;\text{None of these}\end{array}$