Home
Class 12
MATHS
If |z - 3+ 2i| leq 4, (where i = sqrt-...

If `|z - 3+ 2i| leq 4`, (where `i = sqrt-1`) then the difference of greatest and least values of `|z|` is

A

`2sqrt(11)`

B

`3sqrt(11)`

C

`2sqrt(13)`

D

`3sqrt(13)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`|z-3+2i| le 4 rArr |z-(3-2i)|le 4`
This represents the set of all points lying inside or on the circle `|z-(3-2i)|=4`. We have to find the difference between the distances of the points which are farthest and nearest to the origin.

Clearly, Least value of `|z|=OP=CP-OC=4-sqrt(13)`
Greatest value of `|z|=OQ=OC+CQ=4+sqrt(13)`
`therefore` Required difference `=(4+sqrt(13))-(4-sqrt(13))=2sqrt(13)`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|141 Videos

  • COMPLEX NUMBERS

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

If |z-3+2i|<=4, (where i=sqrt(-)1) then the difference of greatest and least values of |z| is

Least value of |z-2|+|z-4i| is

If |z+4|<=3 then find the greatest and least values of |z+1|

|z+3|<=3, then the greatest and least value of |z+1| are

1.If |z-2+il=<2 then find the greatest and least value of z|

1.If |z-2+il=<2 then find the greatest and least value of z|

If |z-i|<=5 and z_(1)=5+3i (where,i=sqrt(-)1) ,then greatest and least values of |iz+z_(1)|

If |z – 2 + i| ge2 , then find the greatest and least value of |z|.

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
  1. If |z - 3+ 2i| leq 4, (where i = sqrt-1) then the difference of grea...

    Text Solution

    |

  2. The locus of the center of a circle which touches the circles |z-z1|=a...

    Text Solution

    |

  3. If n1, n2 are positive integers, then (1 + i)^(n1) + ( 1 + i^3)^(n1) +...

    Text Solution

    |

  4. The modulus of sqrt(2i)-sqrt(-2i) is

    Text Solution

    |

  5. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

    Text Solution

    |

  6. The value of (1+isqrt(3))/(1-isqrt(3))^(6)+(1-isqrt(3))/(1+isqrt(3))^(...

    Text Solution

    |

  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

    Text Solution

    |

  8. If cosA+cosB+cosC=0,sinA + sinB + sinC=0and A+B+C=180^0, then the valu...

    Text Solution

    |

  9. The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omeg...

    Text Solution

    |

  10. The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+...

    Text Solution

    |

  11. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

    Text Solution

    |

  12. The expression (1+i)^(n1)+(1+i^(3))^(n(2)) is real iff

    Text Solution

    |

  13. |{:("6i " "-3i " "1" ),("4 " " 3i" " -1"),("20 " "3 " " i"):}|=x+iy th...

    Text Solution

    |

  14. The centre of a square ABCD is at z0dot If A is z1 , then the centroid...

    Text Solution

    |

  15. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

    Text Solution

    |

  16. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

    Text Solution

    |

  17. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

    Text Solution

    |

  18. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

    Text Solution

    |

  19. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

    Text Solution

    |

  20. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

    Text Solution

    |

  21. The vertices of a square are z1,z2,z3 and z4 taken in the anticlockwis...

    Text Solution

    |