Question
Question: If z = x + iy, and \(w = \frac{1 - iz}{z - i},\) then w = 1 implies that in the complex plane...
If z = x + iy, and w=z−i1−iz, then w = 1 implies that in the complex plane
A
Z lies on the imaginary axis
B
Z lies on the real axis
C
Z lies on the unit circle
D
None of these
Answer
Z lies on the real axis
Explanation
Solution
Sol. As |w| = 1 ⇒ |z – i| = |1 – iz| = |z + i| ⇒ z lies on the right bisector of the line segment connecting the points i and – i. Thus ‘z’ lies on the real axis