Home
Class 11
MATHS
Find the minimum value of the expression...

Find the minimum value of the expression `E= |z|^2+ |z-3|^2 + |z- 6i|^2` (where `z=x+iy, x,y in R`)

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

Find the minimum value of |z-1| if ||z-3|-|z+1||=2.

Solve :z+|z|=1+2i , where z=x+iy,x,yinRR .

For any complex number z find the minimum value of |z|+|z-2i|

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

z is a complex number. The minimum value of |z | + I z - 2| is

If z=x+iy (x, y in R, x !=-1/2) , the number of values of z satisfying |z|^n=z^2|z|^(n-2)+z |z|^(n-2)+1. (n in N, n>1) is

If |z+2|le2, find the maximum and minimum values of |z| .

If z is a complex number, then find the minimum value of |z|+|z-1|+|2z-3|dot

Find the angle between the lines 2x=3y=-z and 6x=-y=-4z

If |z+2|le2 ,find the maximum and minimum values |z|.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z +2 - i|=5 then the maximum value of |3z+9-7i| is K, then find k

    Text Solution

    |

  2. If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in ...

    Text Solution

    |

  3. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

    Text Solution

    |

  4. The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and a...

    Text Solution

    |

  5. If alpha!=betaa n dalpha^2=5alpha-3a n dbeta^2=5beta-3. find the equat...

    Text Solution

    |

  6. Express 1/(1-costheta+2isintheta) in the form x+i y .

    Text Solution

    |

  7. a ,b ,c are three complex numbers on the unit circle |z|=1, such that ...

    Text Solution

    |

  8. If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the eq...

    Text Solution

    |

  9. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R...

    Text Solution

    |

  10. If |z1|=15 and |z2-3-4i|=5,t h e n

    Text Solution

    |

  11. Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x...

    Text Solution

    |

  12. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)

    Text Solution

    |

  13. A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If ...

    Text Solution

    |

  14. If alpha,beta are the roots of the equation a x^2+b x+c=0, then find t...

    Text Solution

    |

  15. If (pi)/2 < alpha < (3pi)/2 then the modulus argument of (1+cos 2alpha...

    Text Solution

    |

  16. The value of z satisfying the equation logz+logz^2+dot+logz^n=0 i s ...

    Text Solution

    |

  17. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  18. find the differtiation of sin(tanx)

    Text Solution

    |

  19. Roots of the equation are (z+1)^5=(z-1)^5 are (a) +-itan(pi/5),+-ita...

    Text Solution

    |

  20. Find the value of a for which one root of the quadratic equation (a^2-...

    Text Solution

    |