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

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