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The maximum value of |a r g(1/(1-z))|for...

The maximum value of `|a r g(1/(1-z))|for|z|=1,z!=1` is given by.

A

`pi/6`

B

`pi/3`

C

`pi/2`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `omega=1/(1-z)`. Then, `z=1-1/omega`
`therefore |z|-1 rArr |1-1/omega|-1 rArr |omega-1|-|omega|`

Thus, the locus of `omega` is perpendicular bisector of the line segment joining (0,0) and (1,0)
Hence, arg `(omega) to pi/2` as `z to 1`.
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