Home
Class 12
MATHS
If the complex numbers z(1), z(2)" and "...

If the complex numbers `z_(1), z_(2)" and "z_(3)` denote the vertices of an isoceles triangle, right angled at `z_(1), " then "(z_(1)-z_(2))^(2)+(z_(1)-z_(3))^(2)` is equal to

A

`0`

B

`(z_(2)+z_(3))^(2)`

C

`2`

D

`(z_(2)- z_(3))^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos

  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos

  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled trianglewith right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

Let z_(1)=3+4i" and "z_(2)= -1+2i . Then |z_(1)+z_(2)|^(2)-2(|z_(1)|^(2)+|z_(2)|^(2)) is equal to

Let the complex numbers z_(1),z_(2),z_(3)" and "z_(4) denote the vertices of a square taken in order. If z_(1)=3+4i" and "z_(3)=5+6i , then the other two vertices z_(2)" and "z_(4) are respectively

Suppose z_(1),z_(2)andz_(3) are the vertices of an equilateral triangle inscribed in the circle |z| = 2. If z_(1)=1+isqrt3 then find z_(2)andz_(3) .

If z_0 is the circumcenter of an equilateral triangle with vertices z_1, z_2, z_3 then z_1^2+z_2^2+z_3^2 is equal to

If z_(1)= 2sqrt(2)(1+i)" and "z_(2)=1+isqrt(3) , then z_(1)^(2)z_(2)^(3) is equal to

If z_(1),z_(2),z_(3) are the vertices of a parallelogram, then the fourth vertex z_(4) opposite to z_(2) is _____

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals:

If z_(1)=2-i, z_(2)=1+i , find |(z_(1)+z_(2)+1)/(z_(1)-z_(2)+1)| .

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If z= e^((2pi i)/(3)), then 1+z+3z^(2)+2z^(3)+2z^(4)+3z^(5) is equal t...

    Text Solution

    |

  2. If z(1)= 2sqrt(2)(1+i)" and "z(2)=1+isqrt(3), then z(1)^(2)z(2)^(3) is...

    Text Solution

    |

  3. If the complex numbers z(1), z(2)" and "z(3) denote the vertices of an...

    Text Solution

    |

  4. If the roots of x^(2)-ax+b=0 are two consecutive odd integers, then a^...

    Text Solution

    |

  5. If alpha" and "beta are the roots of x^(2)-ax+b^(2)=0, then alpha^(2)+...

    Text Solution

    |

  6. If alpha" and "beta are the roots of the equation x^(2)+3x-4=0, then ...

    Text Solution

    |

  7. The value of x such that 3^(2x)-2(3^(x+2))+81=0 is

    Text Solution

    |

  8. If the roots of the equation x^(2)+2bx+c=0 are alpha" and "beta, " the...

    Text Solution

    |

  9. The equation whose roots are the squares of the roots of the eqation 2...

    Text Solution

    |

  10. z and omega are two nonzero complex number such that |z|=|omega|" and ...

    Text Solution

    |

  11. If |z-4| lt |z-2|, its solution is given by

    Text Solution

    |

  12. The locus of the centre of a circle which touches the circle |z-z(1)|=...

    Text Solution

    |

  13. If alpha ne beta" but "alpha^(2)=5 alpha-3" and "beta^(2)= 5 beta-3 th...

    Text Solution

    |

  14. Difference between the corresponding roots of x^(2)+ax+b=0" and "x^(2)...

    Text Solution

    |

  15. Product of real roots of the equation x^(2)+|x|+9=0

    Text Solution

    |

  16. If p and q are the roots of the equation x^(2)+px+q=0, then

    Text Solution

    |

  17. If a,b , c are distinct +ve real numbers and a^(2)+b^(2)+c^(2)=1" then...

    Text Solution

    |

  18. The value of a for which one root of the quadratic equation (a^(2)-5a+...

    Text Solution

    |

  19. If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equ...

    Text Solution

    |

  20. The number of real solution of the equation x^(2)-3|x|+2=0 is

    Text Solution

    |