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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 the imaginary axis

B

z lies on the real axis

C

z lies on the unit circle

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since `|w| =1 rArr |(1-iz)/(z-i)|=1`
`rArr |z-i|=|1-iz|`
`rArr |z-i|=|z+i| [ therefore |1-iz|=|-i||z+i|=|z+i|]`
`therefore` It is a perpendicular bisector of (0,1)
i.e. X-axis .Thus z lies on the real axis
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IIT JEE PREVIOUS YEAR-COMPLEX NUMBERS-TOPIC 2 CONJUGATE AND MODULUS OF A COMPLEX NUMBER (OBJECTIVE QUESTION I)(Only one correct option )
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  11. For positive integer n1,n2 the value of the expression (1+i)^(n1) +(1+...

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  12. The complex number sin(x)+icos(2x) and cos(x)-isin(2x) are conjugate t...

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  13. The points, z1,z2,z3,z4, in the complex plane are the vartices of a pa...

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  14. If z=x+iy and w=(1-iz)/(z-i), then |w|=1 implies that in the complex ...

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