Home
Class 12
MATHS
For all complex numbers z1,z2 satisfyin...

For all complex numbers `z_1,z_2` satisfying `|z_1|=12` and `|z_2-3-4i|=5`, find the minimum value of `|z_1-z_2|`

Text Solution

Verified by Experts

form figure minimum `| z_(1)-z_(2)| = PQ`
` |z_(1) -z_(2)| = PQ ge OQ -OP = 12 -10 =2 `
`Rightarrow min |z_(1) -z_(2)| =2`
Second Method.
we have,
`|z_(1)-z_(2)|=|z_(1)-(z_(2)-3-4i)+3+4i|`
` ge|z_(1)| -|z_(2) -3-4i|-|3+4|`
[ using ` |z_(1) -z_(2)|ge | |z_(1)| -|z_(2)|]`
` ge 12 -5-5=2`
i.e, ` |z_(1)-z_(2)|ge 2 `
` Rightarrow min |z_(1) -z_(2)| =2`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos

Similar Questions

Explore conceptually related problems

For all complex numbers z_(1),z_(2) satisfying |z_(1)|=12 and |z_(2)-3-4i|=5, find the minimum value of |z_(1)-z_(2)|

For all complex numbers z_(1),z_(2) satisfying |z_(1)|=12 and |z_(2)-3-4i|=5, the minimum value of |z_(1)-z_(2)| is

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 the minimum value of |z_1-z_2| is (A) 0 (B) 2 (C) 7 (D) 17

For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4 iota|=5, the minimum value of |z1-z2| is: a.0 b.2c.7d .

Let z_1 and z_2 be two complex numbers satisfying |z_1|=9 and |z_2-3-4i|=4 Then the minimum value of |z_1-Z_2| is

Let z _(1) and z _(2) be two complex numberjs satisfying |z _(1)|=3 and |z _(2) -3-4i|=4. Then the minimum value of |z_(1) -z _(2)| is

For all complex number z_(1),z_(2) satisfying |z_(1)|=12 and |z_(2)-3-4 iota|=5, then |z_(2)-iota z_(1)|

Let Z_(1) and Z_(2) be two complex numbers satisfying |Z_(1)|=9 and |Z_(2)-3-4i|=4 . Then the minimum value of |Z_(1)-Z_(2)| is

AAKASH INSTITUTE-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-section-J (Aakash Challengers Qestions)
  1. For all complex numbers z1,z2 satisfying |z1|=12 and |z2-3-4i|=5, fin...

    Text Solution

    |

  2. Let n be even postiive integer such that n/2 is odd and let alpha(0)...

    Text Solution

    |

  3. Let z(1),z(2),z(3) be complex numbers, not all real, such that |z(1)|...

    Text Solution

    |

  4. Let z(1),z(2),z(3) be complex numbers, such that (i) |z(1)|=|z(2)...

    Text Solution

    |

  5. find all complex numbers z such that |z -|z+1|| = |z+|z-1||

    Text Solution

    |

  6. Suppose p is a polynomial with complex coefficients and an even degree...

    Text Solution

    |

  7. The point A(1),A(2)…… A(10) are equally distributed on a circle of rad...

    Text Solution

    |

  8. Let a and b be positive real numbers with a^(3) +b^(3) = a -b and k...

    Text Solution

    |

  9. Let k be a real number such that the inequality sqrt(x-3) +sqrt(6 -x)...

    Text Solution

    |

  10. If alpha and beta are the roots of the equation x^2 + px -1/(2p^2) =...

    Text Solution

    |

  11. If the roots of the quadratic equation x^2 - ax + 2b = 0 are prime num...

    Text Solution

    |

  12. The number of real solutions of the equation root4(97-x) + root4(x) =5...

    Text Solution

    |

  13. If f(x) is a polynomial of degree at least two with integral co-effic...

    Text Solution

    |

  14. p=(x(1)-x(2))^(2) +(x(1)-x(3))^(2) + .......+(x(1)-x(6))^(2) +(x(2)-x(...

    Text Solution

    |

  15. If x,y,z are three real numbers such that x+ y +z =4 and x^(2) + y^(2...

    Text Solution

    |

  16. If unity is double repeated root of px^3+ g(x^2 + x) +r=0, then

    Text Solution

    |

  17. The number of real solutions of the equation 4x^(99) +5x^(98) + 4x^(9...

    Text Solution

    |