Home
Class 12
MATHS
|z - i | <= 2 and z0 = 5 + 3i then max. ...

`|z - i | <= 2` and `z_0 = 5 + 3i` then max. value of `|iz+z_0|` is :

A

`2+sqrt(31)`

B

7

C

`sqrt(31)-2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`|iz+z_(0)|=|i||z-iz_(0)|=|z-5i+3|=|z-i+3-4i|`
`rArr |iz+z_(0)| le |z-i|+3-4i| le 2+5=7`
Hence, the maximum value of `|iz+z_(0)|` is 7.
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

If |z + i| = |z - i|, prove that z is real.

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

The equation |z - i| = |z - 1| represents :

Eccentricity of conic |z - 5i| + |z + 5i| = 25 is ___________.

The inequality |z-i| lt |z + i| represents the region

If z in C and 2z = |z| + i , then z equals

OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Section I - Solved Mcqs
  1. Complex numbers z(1) and z(2) lie on the rays arg(z1)=theta and arg(z1...

    Text Solution

    |

  2. If z is a complex number satisfying |z|^(2)-|z|-2 lt 0, then the value...

    Text Solution

    |

  3. |z - i | <= 2 and z0 = 5 + 3i then max. value of |iz+z0| is :

    Text Solution

    |

  4. If |z|= "max"{|z-2|,|z+2|}, then

    Text Solution

    |

  5. if |(z-6)/(z+8)|=1, then the value of x in R, where z=x+i|{:(-3,2i,2+i...

    Text Solution

    |

  6. If |z-1|+|z+3|<=8, then the range of values of |z-4| is

    Text Solution

    |

  7. The equation |z-i|+|z+i|=k, k gt 0 can represent an ellipse, if k=

    Text Solution

    |

  8. Find the range of K for which the equation |z+i| - |z-i | = K represen...

    Text Solution

    |

  9. If |z+3i|+|z-i|=8, then the locus of z, in the Argand plane, is

    Text Solution

    |

  10. In Fig. 42, a point 'z' is equidistant from three distinct points z(1)...

    Text Solution

    |

  11. Let P(e^(itheta1)), Q(e^(itheta2)) and R(e^(itheta3)) be the vertices...

    Text Solution

    |

  12. If A(z(1)),B(z(2)), C(z(3)) are the vertices of an equilateral triangl...

    Text Solution

    |

  13. If A (z1), B (z2) and C (z3) are three points in the argand plane whe...

    Text Solution

    |

  14. If a1,a2 ...an are nth roots of unity then1/(1-a1) +1/(1-a2)+1/(1-a3)....

    Text Solution

    |

  15. Let A(z(1)) and B(z(2)) be such that angleAOB=theta('O') being the ori...

    Text Solution

    |

  16. If one root of z^2 + (a + i)z+ b +ic =0 is real, where a, b, c in R , ...

    Text Solution

    |

  17. If A and B represent the complex numbers z(1) and z(2) such that |z(1)...

    Text Solution

    |

  18. If z1, lies in |z-3|<=4,z2 on |z-1|+|z+1|=3 and A = |z1-z2|, then :

    Text Solution

    |

  19. Let O, A, B be three collinear points such that OA.OB=1. If O and B re...

    Text Solution

    |

  20. If z(0),z(1) represent points P and Q on the circle |z-1|=1 taken in a...

    Text Solution

    |