Home
Class 11
MATHS
if z1, z2, z3 are the vertices pf an equ...

if `z_1, z_2, z_3` are the vertices pf an equilateral triangle inscribed in the circle `absz=1` and `z_1=i`, then

A

`z_2=-((sqrt3+i)/2)`

B

`z_3=sqrt3/2+i/2`

C

`z_2=-1/2-isqrt3/2`

D

`z_3=(sqrt3-i)/2

Text Solution

Verified by Experts

The correct Answer is:
A, D
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

Suppose that z_1, z_2, z_3 are three vertices of an equilateral triangle in the Argand plane let alpha=1/2(sqrt3+i) and beta be a non zero complex number the point alphaz_1+beta,alphaz_2+beta,alphaz_3+beta wil be

If z_1,z_2,z_3 are the vertices of an equilateral triangle with z_0 as its circum centre, the changing origin to z_0 new vertices become z_1',z_2',z_3' show that z_1'^2+z_2'^2+z_3'^2=0

A(z_1),B(z_2),C(z_3) are the vertices a triangle ABC inscribed in the circle abs(z)=2 internal angle bosector of the angle A meet the circumference again at D(z_4) then prove z_4^2=z_2z_3

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:

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle then prove that z_1^2+z_2^2+z_3^2=3z_0^2

If z_1,z_2,z_3 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

Suppose that z_(1), z_(2), z_(3) are three vertices of an equilateral triangle in the Argand plane. Let alpha=(1)/(2) (sqrt(3) +i) and beta be a non-zero complex number. The point alphaz_(1) +beta, alpha z_(2)+beta, az_(3)+beta will be

If A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

If the points A(z),B(-z),C(1-z) are the vertices of an equilateral triangle ABC then Re(z) is

Suppose that z_(1),z_(2),z_(3) are three vertices of an equilateral triangle in the Angand plane . Ley alpha=(1)/(2)(sqrt(3)+i)andbeta be a non-zero complex number . The points alphaz_(1)+beta,alphaz_(2)+beta,alphaz_(3)+beta will be -

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. The value of underset(k=1)overset10sum(-sin((2kpi)/11)+icos((2kpi)/11)...

    Text Solution

    |

  2. If amp(z1z2)=0 and absz1=absz2=1, then

    Text Solution

    |

  3. if z1, z2, z3 are the vertices pf an equilateral triangle inscribed in...

    Text Solution

    |

  4. if amp (z-1)/(z+1)=pi/3, then the locus of z is

    Text Solution

    |

  5. If e^(ialpha)=cosalpha+isinalpha, then for the DeltaABC, the value of ...

    Text Solution

    |

  6. The equation zbarz+(4-3i)z+(4+3i)barz+5=0 represents a circle of radiu...

    Text Solution

    |

  7. Let z1 and z2 be two distinct complex numbers and let z= (1-t)z1+tz2 f...

    Text Solution

    |

  8. The roots of the equation Z^3+1=0 are called cube roots of unity.Clear...

    Text Solution

    |

  9. The roots of the equation Z^3+1=0 are called cube roots of unity.Clear...

    Text Solution

    |

  10. LetA(z1),B(z2) and C(z3) be the three points in Argands plane The po...

    Text Solution

    |

  11. LetA(z1),B(z2) and C(z3) be the three points in Argands plane The po...

    Text Solution

    |

  12. Match List - I with List-II

    Text Solution

    |

  13. Match List - I with List-II

    Text Solution

    |

  14. If Argzlt0 then (Arg(-z)-Arg(z))/(pi(cos(pi/3)) is equal to

    Text Solution

    |

  15. If s(n)=i^n+i^(-n) where i=sqrt(-1) and n is an integer then the total...

    Text Solution

    |

  16. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

    Text Solution

    |

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

    Text Solution

    |

  18. Ifomega is a nonreal cube root of unity then (a+bomega+cw^2)/(c+aome...

    Text Solution

    |

  19. If(cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show...

    Text Solution

    |

  20. If(cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show...

    Text Solution

    |