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 ENGLISH|Exercise Section I - Solved Mcqs|141 Videos

  • COMPLEX NUMBERS

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

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

Similar Questions

Explore conceptually related problems

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

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

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

1. If |z-2+i|≤ 2 then find the greatest and least value of | z|

1. If |z-2+i| ≤ 2 then find the greatest and least value of | z|

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

If |z-4/z|=2 then the greatest value of |z| is:

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

If |z-4 +3i| le 2 then the least and the greatest values of |z| are q

Let z be a complex number satisfying 1/2 le |z| le 4 , then sum of greatest and least values of |z+1/z| is :

OBJECTIVE RD SHARMA ENGLISH-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. Prove that for positive integers n(1) and n(2), the value of express...

    Text Solution

    |

  4. The value of abs(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+ i sqrt(3))/(1-isqrt(3)))+ ((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=0andA+B+C=180^(@) then the value of...

    Text Solution

    |

  9. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

    Text Solution

    |

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

    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))^(n2) is real iff

    Text Solution

    |

  13. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

    Text Solution

    |

  14. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

  15. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

    Text Solution

    |

  21. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |