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Equation of tangent drawn to circle abs(...

Equation of tangent drawn to circle `abs(z)=r` at the point `A(z_(0))`, is

A

`Re((z)/(z_(0))=1`

B

`zbarz_(0)+ z_(0)barz = 2r^(3)`

C

`Im((z)/(z_(0))=1`

D

`Im((z_(0))/(z))=1`

Text Solution

Verified by Experts

The correct Answer is:
A, B

`/_ OAP = (pi)/(2)`
`rArr (z-z_(0))/(z_(0))=0` is purely imaginary
`rArr (z- z_(0))/(z_(0)) + (barz-barz_(0))/(z_(0)) + (barz-barz_(0))/(barz_(0))=0`
`or (z)/(z_(0)) + (barz)/(barz_(0)) = 2" "(0)`
`rArr Re((z)/(z_(0))) = 1`
From (1),
`zbarz_(0) + z_(0)barz= 2|z_(0)|^(2) = 2r^(2)`
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