Home
Class 12
MATHS
A complex number z is said to be unimodu...

A complex number z is said to be unimodular if `abs(z)=1`. Suppose `z_(1)` and `z_(2)` are complex numbers such that `(z_(1)-2z_(2))/(2-z_(1)z_(2)^_)` is unimodular and `z_(2)` is not unimodular. Then the point `z_(1)` lies on a

A

straight line parallel to X-axis

B

straight line parallel to Y-axis

C

circle of radius 2

D

circle of radius `sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

If z_1 and z_2 are two complex numbers such that (z_1-2z_2)/(2-z_1bar(z_2)) is unimodular whereas z_1 is not unimodular then |z_1| =

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

If z_(1) and z_(2) are to complex numbers such that two |z_(1)|=|z_(2)|+|z_(1)-z_(2)| , then arg (z_(1))-"arg"(z_(2))

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , then:

Let z_(1),z_(2) be two complex numbers such that z_(1)+z_(2) and z_(1)z_(2) both are real, then

If z_(1) and z_(2) are two complex numbers satisying the equation. |(iz_(1)+z_(2))/(iz_(1)-z_(2))|=1 , then z_(1)/z_(2) is

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then which one of the following is true?

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

If z_(1) ,z_(2) be two complex numbers satisfying the equation |(z_(1)+z_(2))/(z_(1)-z_(2))|=1 , then

Home
Profile