Home
Class 12
MATHS
The set of points z in the complex plane...

The set of points z in the complex plane satisfying `|z-i|z||=|z+i|z||` is contained or equal to the set of points z satisfying

A

`"lm"(z)=0`

B

`"Im"(z) le 1`

C

`|"Re"(z)| le 2`

D

`|z| le 3`

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`|z-i|z||=|z+i|z||`
`|z/(|z|)-i|=|z/(|z|)+i|`
`rArr z/|z|` lies on real axis `rArr "Im"(z/|z|)=0 rArr "Im"(z)=0`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|15 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Exercise|131 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

Similar Questions

Explore conceptually related problems

The point z in the complex plane satisfying |z+2|-|z-2|=+3 lies on

The set of points z |z-i|z||=|z+i|z|| is contained in or equal to

Points z in the complex plane satisfying "Re"(z+1)^(2)=|z|^(2)+1 lie on

The set of points z satisfying |z+4|+|z-4|=0 is contained in or equal to

The set of points z satisfying |z+4|+|z-4|=0 is contained in or equal to

The set of points z satisfying |z+4|+|z-4|=10 is contained or equal to

If |omega|=1 , then the set of points z=omega+1/omega is contained in or equal to the set of points z satisfying.

If |omega|=2 , then the set of points z=omega-1/omega is contained in or equal to the set of points z satisfying

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

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
  1. Let Z1 and Z2, be two distinct complex numbers and let w = (1 - t) z1 ...

    Text Solution

    |

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

    Text Solution

    |

  3. The set of points z in the complex plane satisfying |z-i|z||=|z+i|z|| ...

    Text Solution

    |

  4. The set of points z satisfying |z+4|+|z-4|=10 is contained or equal to

    Text Solution

    |

  5. If |omega|=2, then the set of points z=omega-1/omega is contained in o...

    Text Solution

    |

  6. If |omega|=1, then the set of points z=omega+1/omega is contained in o...

    Text Solution

    |

  7. The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

    Text Solution

    |

  8. Let alpha and beta be real numbers and z be a complex number. If z^(2...

    Text Solution

    |

  9. If omega !=1 is the complex cube root of unity and matrix H=[(omega,...

    Text Solution

    |

  10. The maximum value of |a r g(1/(1-z))|for|z|=1,z!=1 is given by.

    Text Solution

    |

  11. If z is any complex number satisfying |z-3-2i|lt=2 then the maximum va...

    Text Solution

    |

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

    Text Solution

    |

  13. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

    Text Solution

    |

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

    Text Solution

    |

  15. The minimum value of |z(1)-z(2)| as z(1) and z(2) vary over the curves...

    Text Solution

    |

  16. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2(y-y0)^2=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let z(k)=cos(2kpi)/10+isin(2kpi)/10,k=1,2,………..,9. Then, 1/10{|1-z(1)|...

    Text Solution

    |