Home
Class 11
MATHS
If z0 is the circumcenter of an equilate...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

Let z_(0) be the circumcenter of an equilateral triangle whose affixes are z_(1),z_(2),z_(3) . Statement-1 : z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=3z_(0)^(2) Statement-2: z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=2(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))

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 the fourth roots of unity are z_1, z_2, z_3, z_4 and z_1^2+z_2^2+z_3^2+z_4^2 is equal to :

The triangle with vertices at the point z_1z_2,(1-i)z_1+i z_2 is

If z_(1),z_(2) are vertices of an equilateral triangle with z_(0) its centroid, then z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=

if the complex no z_1 , z_2 and z_3 represents the vertices of an equilateral triangle such that |z_1| = | z_2| = | z_3| then relation among z_1 , z_2 and z_3

if the complex no z_1 , z_2 and z_3 represents the vertices of an equilateral triangle such that |z_1| = | z_2| = | z_3| then relation among z_1 , z_2 and z_3

If z_1,z_2,z_3 be the vertices of an equilateral triangle, show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)= 0 or z_1^2+z_2^2+z_3^2= z_1z_2+z_2z_3+z_3z_1 .

Let the complex numbers z_1,z_2 and z_3 be the vertices of a equilateral triangle. Let z_0 be the circumcentre of the tringel ,then z_1^2+z_2^2+z_3^2= (A) z_0^2 (B) 3z_0^2 (C) 9z_0^2 (D) 0

If z_(1),z_(2),z_(3) are the vertices of an equilational triangle ABC such that |z_(1)-i|=|z_(2)- i| = |z_(3)-i|, then |z_(1)+z_(2)+z_(3)| equals to

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Prove that the circles z bar z +z( bar a 1)+bar z( a1 )+b1=0 ,b1 in ...

    Text Solution

    |

  2. If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0...

    Text Solution

    |

  3. If z0 is the circumcenter of an equilateral triangle with vertices z1,...

    Text Solution

    |

  4. Two different non-parallel lines cut the circle |z| = r at points a...

    Text Solution

    |

  5. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

    Text Solution

    |

  6. Prove that |z-z(1)|^(2) + |z - z(2)|^(2) = a will represent a real ci...

    Text Solution

    |

  7. Complex numbers z1 , z2 , z3 are the vertices A, B, C respectively of ...

    Text Solution

    |

  8. Given that alpha , gamma are roots of the equation Ax^(2) - 4x + 1 ...

    Text Solution

    |

  9. Show that the area of the triangle on the Argand diagram formed by the...

    Text Solution

    |

  10. Intercept made by the circle zbar z +bar a+abar z+r=0 on the real a...

    Text Solution

    |

  11. The graph of the quadratic trinomial u=a x^2+b x+c has its vertex at (...

    Text Solution

    |

  12. Show that if iz^3+z^2-z+i=0, then |z|=1

    Text Solution

    |

  13. Show that the equation of a circle passing through the origin and ha...

    Text Solution

    |

  14. The function f(x)=a x^2+b x^2+c x+d has three positive roots. If the ...

    Text Solution

    |

  15. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

    Text Solution

    |

  16. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

    Text Solution

    |

  17. If (18 x^2+12 x+4)^n=a0+a(1x)+a2x2++a(2n)x^(2n), prove that ar=2^n3^r(...

    Text Solution

    |

  18. If z=z0+A( bar z -( bar z 0)), w h e r eA is a constant, then prove t...

    Text Solution

    |

  19. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

    Text Solution

    |

  20. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, t...

    Text Solution

    |