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$z = x + iy and w = \frac{1 - iz}{z - i}, then | w | = 1 \Rightarrow$ In the complex plane

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z lies on the imaginary axis

z lies on the parabola

z lies on the unit circle

z lies on the real axis

answer is B.

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Detailed Solution

$Wi = \frac{z + i}{z - i} \Rightarrow | z + i | = | z - i |$
z lies on perpendicular bisector of (0, –1) and (0, 1) i.e. x axis (Real axis)

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