Home
Class 12
MATHS
Let z(1) and z(2) be two distinct comple...

Let `z_(1)` and `z_(2)` be two distinct complex numbers and `z=(1-t)z_(1)+iz_(2)`, for some real number t with `0 lt t lt 1` and `i=sqrt(-1)`. If arg(w) denotes the principal argument of a non-zero compolex number w, then

A

`|z - z_(1)| + |z-z_(2)| = |z_(1) - z_(2)|`

B

Arg `(z - z_(1)) = "Arg" (z-z_(2))`

C

`|(z-z_(1),bar(z)-bar(z)_(1)),(z_(2)-z_(1),bar(z)_(2)-bar(z)_(1))|=0`

D

`Arg (z - z_(1)) = Arg (z_(2) - z_(1))`

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES LEVEL 5|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES LEVEL 6|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES LEVEL 3|1 Videos

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

Let Z_1 and Z_2 , be two distinct complex numbers and let w = (1 - t) z_1 + t z_2 for some number "t" with o

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

Knowledge Check

  • If z_(1) , z_(2) be two distinct complex numbers and let z = (1 - t) z_(1) + tz_(2) for some real number t with 0 lt t lt 1 . If arg (omega) denotes the principal argument of a non - zero complex number omega then

    A
    `|z - z_(1)| + | z - z_(2)\ = | z_(1) - z_(2)|`
    B
    `arg ( z - z_(1)) = arg ( z - z_(2))`
    C
    `|(z - z_(1),bar(z)-bar(z)_(1)),(z_(2)-z_(1),bar(z)_(2)-bar(z)_(1))|=0`
    D
    `arg (z - z_(1)) = arg ( z _(2) - z_(1))`

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

    A
    `z_(1)=-z_(2)`
    B
    `z_(1)=barz_(2)`
    C
    `z_(1)=-barz_(2)`
    D
    `z_(1)=z_(2)`

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

    A
    arg`(z_(1))="arg"(z_(2))`
    B
    `"arg"(z_(1))+"arg"(z_(2))=pi/2`
    C
    `|z_(1)|=|z_(2)|`
    D
    `z_(1)z_(2)=1`

    • Similar Questions

    Explore conceptually related problems

    If Z_(1),Z_(2) are two complex numbers such that Z_(1)+Z_(2) is a complex no and Z_(1)Z_(2) is real number

    If z_(1)-z_(2) are two complex numbers such that |(z_(1))/(z_(2))|=1 and arg (z_(1)z_(2))=0, then

    Let z_(1) and z_(2) be two complex numbers such that bar(z)_(1)+bar(iz)_(2)=0 and arg(z_(1)z_(2))=pi then find arg(z_(1))

    If arg (z-z_1)/(z_2-z_1) = 0 for three distinct complex numbers z,z_1,z_2 then the three points are

    If z_(1) and z_(2) be two complex numbers such that | z_(1) - z_(2)| = | z_(1)| - | z_(2)| , then arg (z_(1))/( z_(2)) is

    Home
    Profile