Home
Class 12
MATHS
Let O, A, B be three collinear points su...

Let `O`, `A`, `B` be three collinear points such that `OA.OB=1`. If `O` and `B` represent the complex numbers `O` and `z`, then `A` represents

A

`(1)/(barz)`

B

`(1)/(z)`

C

`barz`

D

`z^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` Let `A` represents `z_(1)`.
Since `OA.OB=1 :. |z_(1)-0|.|z-0|=1`
`implies |z_(2)|=(1)/(|z|)`
Also, `arg((z_(1)-0)/(z-0))=0impliesarg((z_(1))/(z))=0`
`impliesargz_(1)=argz`
If `theta` is the argument of `z`, then
`z=|z|e^(itheta)`
`:. z_(1)=(1)/(|z|)e^(etheta)=(1)/(|z|^(2))|z|e^(itheta)-(z)/(zbarz)=(1)/(barz)`
`:. A` is `(1)/(baraz)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

Represent the complex number z=1+isqrt(3) in the polar form.

Let a , b , c be distinct complex numbers with |a|=|b|=|c|=1 and z_(1) , z_(2) be the roots of the equation az^(2)+bz+c=0 with |z_(1)|=1 . Let P and Q represent the complex numbers z_(1) and z_(2) in the Argand plane with /_POQ=theta , o^(@) lt 180^(@) (where O being the origin).Then

If z ne 1 and (z^2)/(z-1) is real then the point represented by the complex number z lies

If |z-1-i|=1 , then the locus of a point represented by the complex number 5(z-i)-6 is

The points representing the complex number z for which arg((z-2)/(z+2))=pi/3 lie on

If zne1and(z^(2))/(z-1) is real , then the point represented by the complex number z lies -

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on -

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on

Find the locus of the points representing the complex number z for which |z+5|^2-|z-5|^2=10.

Let z be a complex number satisfying |z+16|=4|z+1| . Then