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Let `A(z_(1))` and `B(z_(2))` are two distinct non-real complex numbers in the argand plane such that `(z_(1))/(z_(2))+(barz_(1))/(z_(2))=2`. The value of `|/_ABO|` is

A

`(pi)/(6)`

B

`(pi)/(4)`

C

`(pi)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(z_(1))/(z_(2))+(barz_(1))/(barz_(2))=2`
`impliesRe((z_(1))/(z_(2)))=1`
Let `(z_(1))/(z_(2))=x+iyimpliesx=1`
Now, `arg((z_(1)-z_(2))/(-z_(2)))=arg(1-(z_(1))/(z_(2)))=arg(-iy)=+-(pi)/(2)`
`/_ABO=(pi)/(2)`
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