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If |z|=1 and z ne +-1, then one of the p...

If `|z|=1` and `z ne +-1`, then one of the possible value of `arg(z)-arg(z+1)-arg(z-1)` , is

A

`-pi//6`

B

`pi//3`

C

`-pi//2`

D

`pi//4`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `arg(z)-arg(z+1)-arg(z-1)`
`=arg((z)/(z^(2)-1))`
`=arg((z)/(z^(2)-zbarz))`
`=arg((1)/(z-barz))`
`=arg` (purely imaginary no.)
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