Home
Class 12
MATHS
If |z|=1 and z ne +-1, then one of the p...

If `|z|=1` and `z ne +-1`, then one of the possible value of `arg(z)-arg(z+1)-arg(z-1)` , is

A

`-pi//6`

B

`pi//3`

C

`-pi//2`

D

`pi//4`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `arg(z)-arg(z+1)-arg(z-1)`
`=arg((z)/(z^(2)-1))`
`=arg((z)/(z^(2)-zbarz))`
`=arg((1)/(z-barz))`
`=arg` (purely imaginary no.)
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

If z =(-2)/(1+sqrt3i), then the value of arg(z) is-

If absz=1 and z ne+-1 then all the values of z/(1-z^2) lie on

If |z|=1 and z'=(1+z^(2))/(z) , then

If abs(z-1)+abs(z+3)le8 then possible value of abs(z-4) is

If z_(1)=3i and z_(2)=-1-i , where i=sqrt(-1) find the value of arg ((z_(1))/(z_(2)))

In complex plane z_(1), z_(2) and z_(3) be three collinear complex numbers, then the value of |(z_(1),barz_(1),1),(z_(2),barz_(2),1),(z_(3), barz_(3),1)| is -

Let z be a complex number such that the principal value of argument, argzgt0 . Then argz-arg(-z) is

If z and w are two nonzero complex numbers such the abs(zw)=1 and arg(z)-arg(w)=pi/2 then barzw is equal to

If z=(sqrt(5-12i)+sqrt(-5-12i)), then the principal value of arg z will be

If |z-3|=min{|z-1|,|z-5|}, then the values of Re(z) will be