Let OP.OQ=1 and let O,P and Q be three collinear points. If O and Q represent the complex numbers of origin and z respectively, then P represents

Options

A. `1/z`
B. `barz`
C. `1/barz`
D. `-z`

Answer

C

Explanation

Let P represent the complex number `z_(1)`
Let `z=re^(itheta)`. Then, OQ=r and arg(z)=`theta`
Since, O,P and Q are collinear points. Therefore,
`"arg"(z_(1))=theta` or `pi+theta`
`rArr z_(1)=OP e^(itheta)` or, `z_(1)=Ope^(i(pi+theta))`
`rArr z_(1)=(OP.OQ)/(OQ)e^(itheta)` or, `z_(1)=(1/(OQe^(-itheta))` or `z_(1)=-1/(OQe^(-itheta))`
`rArr z_(1)=1/(re^(itheta))` or `z_(1)=-1/(re^(itheta))`
`rArr z=1/barz` or `z_(1)=-1/barz`