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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

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`w = (1-iz)/(z-i)`
`=>|w| = |(1-iz)|/|(z-i)|`
`=>|w|^2 = |(1-iz)|^2/|(z-i)|^2`
`=>|w|^2 = |(1-i(x+iy))|^2/(|(x+iy)-i|^2`
`=>1^2 = |(1+y) - ix|^2/|x+(y-1)i|^2`
`=>x^2+(y-1)^2 = x^2+(1+y)^2`
`=>y-1 = 1+y`
`=> y = 0`
...
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