Home
Class 11
MATHS
The value of absz^2+abs(z-3)^2+abs(z-i)^...

The value of `absz^2+abs(z-3)^2+abs(z-i)^2` is minimum when z equals

A

2-(2/3)i

B

45+3i

C

1+(i/3)

D

1-(i/3)

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

The value of |z|^(2)+|z-3|^(2)+|z-i|^(2) is minimum when z equals -

If z_1 and z_2 be two complex numbers such that abszle1, absz_2le1, abs(z_1+iz_2)=abs(z_1-iz_2)=2 , then z_1 equals

If absz=min{abs(z-1), abs(z+1)} , then

abs(z-6)ltabs(z-2) its solution is given by

z_1, z_2, z_3 are three points lying on the circle absz=1 , maximum value of abs(z_1-z_2)^2+abs(z_2-z_3)^2+abs(z_3-z_1)^2 is

If abs(z^2-1)=absz^2+1 , then z lies on

Find the maximum value of absz when abs(z-3/z)=2 ,z being a complex number

The system of equations abs(z+1-i)=sqrt2 ,absz=3 has

If abs(z-2-2i)=1 , then the minimum value of absz is

For all complex niumbers z_1, z_2 satisfying absz_1=12 and abs(z_2-3-4i)=5 , the minimum value of abs(z_1-z_2) is

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a comple...

    Text Solution

    |

  2. Suppose that z1, z2, z3 are three vertices of an equilateral triangle ...

    Text Solution

    |

  3. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

    Text Solution

    |

  4. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

    Text Solution

    |

  5. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

    Text Solution

    |

  6. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

    Text Solution

    |

  7. If z is a complex number of unit modulus and argument theta then arg(...

    Text Solution

    |

  8. Let z1=2+3i and z2=3+4i be two points on the complex plane then the se...

    Text Solution

    |

  9. Suppose z=x+iy where x and y are real numbers and i=sqrt(-1) the point...

    Text Solution

    |

  10. If P,Q,R are angles of an isosceles triangle and anglep=pi/2 then the ...

    Text Solution

    |

  11. Let z be a complex number such that the imaginary part of z is non zer...

    Text Solution

    |

  12. If z ne 1 and (z^2)/(z-1) is real then the point represented by the co...

    Text Solution

    |

  13. The maximum value of absz when the complex number z satisfies the cond...

    Text Solution

    |

  14. If (3/2+isqrt3/2)^50=3^25(x+iy)where x and y are real then the order P...

    Text Solution

    |

  15. If (z-1)/(z+1) is purely imaginary then

    Text Solution

    |

  16. The points representing the complex number z for which arg((z-2)/(z+2)...

    Text Solution

    |

  17. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

    Text Solution

    |

  18. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

    Text Solution

    |

  19. If omega(ne1) is a cube root of unity and (1+omega)^7=A+Bomega then (A...

    Text Solution

    |

  20. For the real parameter t,the locus of the complex number z=(1-t^2)+isq...

    Text Solution

    |