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If z is a complex number such that amp ...

If z is a complex number such that amp `("z-2"/"2z+3i")=0` and `z_0`=3+4i, then the value of `z_0z +barz_0 barz` (whenever defined)

A

is 6

B

is 24

C

is 12

D

depends on the value of z

Text Solution

Verified by Experts

The correct Answer is:
C
amp`((z-2)/(2z+3i))=0`
`(z-2)/(2z+3i)=k` (k gt 0 )
z-2=2zk+3ik
`z=(3ik+2)/(1-2k)`
`z_0z+barz_0barz=2Re(z_0z)`
`=2Re((3+4i).((3ik+2)/(1-2k)))`
`2("6-12k"/"1-2k")`
`=2.6"(1-2k)"/"(1-2k)"`
=12
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