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,barz-barz_1),(z_2-z_1,barz_2-barz_1):}|=0`

D

Arg `(z-z_1) = Arg (z_2-z_1) `

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos

  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 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) and z_(1)z_(2) both are real, then

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

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

MOTION-COMPLEX NUMBER -EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED
  1. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  2. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  3. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

    Text Solution

    |

  4. Let omega be the complex number " cos " ( 2pi)/(3) + isin (2pi)/(3)...

    Text Solution

    |

  5. Match the statement in Column I with those in Column II. [Note : He...

    Text Solution

    |

  6. Let a, b and c be three real numbers satisfying [a" "b" "c][[1,9,7],[...

    Text Solution

    |

  7. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

    Text Solution

    |

  8. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  9. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

    Text Solution

    |

  10. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  11. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |

  12. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  13. Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (...

    Text Solution

    |

  14. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

    Text Solution

    |

  15. Let omega be a complex cube root of unity with omegane1 and P = [pij]...

    Text Solution

    |

  16. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  17. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  18. Let zk=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","...

    Text Solution

    |

  19. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

    Text Solution

    |

  20. Let a,b in R and a^(2) + b^(2) ne 0 . Suppose S = { z in C: z = (1...

    Text Solution

    |