if z=x+iy and  w=(1-iz)/(z-i),den w=1 implies tat ,in complex plane

a.z lies on imaginary axis

b.z lies on real axis

c.z lies on the unit circle

d.none

Since

w=1

z-i=1-iz

x+i(y-1)=1-i(x+iy)

x+i(y-1)=1+y-ix

comparing

x=1+y  and  y-1=-x

solve these two eqn's u get

x=1  and y=0

Thus z lies on the real axis  and also on the unit circle