Home
Class 11
MATHS
If absz1=absz2=absz3=1 and z1+z2+z3=0, t...

If `absz_1=absz_2=absz_3=1` and `z_1+z_2+z_3=0`, then `z_1, z_2, z_3` are vertices of

A

a right angled triangle

B

an equilateral triangle

C

isosceles triangle

D

scalene triangle

Text Solution

Verified by Experts

The correct Answer is:
B
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

If |z_1|=|z_2|=|z_3|=1 and z_1+z_2+z_3=0 then the area of the triangle whose vertices are z_1, z_2, z_3 is 3sqrt(3)//4 b. sqrt(3)//4 c. 1 d. 2

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.

Let z_1, z_2, z_3 be three complex numbers and a ,b ,c be real numbers not all zero, such that a+b+c=0 and a z_1+b z_2+c z_3=0. Show that z_1, z_2,z_3 are collinear.

If amp (z_1z_2)=0 and absz_1=absz_2=1 , then

If z_1,z_2, z_3 are complex numbers such that |z_1|=|z_2|=|z_3|=|1/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| is equal to

If z_1 lies on absz=1 and z_2 lies on absz=2 then

The complex numbers z_1,z_2 and z_3 satisfying (z_1-z_3)/(z_2-z_3)=(1-isqrt3)/2 are the verticles of a triangle which is:

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

If z_1 + z_2 + z_3 + z_4 = 0 where b_i in R such that the sum of no two values being zero and b_1 z_1+b_2z_2 +b_3z_3 + b_4z_4 = 0 where z_1,z_2,z_3,z_4 are arbitrary complex numbers such that no three of them are collinear, prove that the four complex numbers would be concyclic if |b_1b_2||z_1-z_2|^2=|b_3b_4||z_3-z_4|^2 .

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then a. z_1 = z_2 b. |z_2|^2 = z_1*z_2 c. z_1*z_2 = 1 d. none of these

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. The origin and the roots of the equation z^2+pz+q=0 form an equilatera...

    Text Solution

    |

  2. If n is a positive integer, then, (1+isqrt3)^n+(1-isqrt3)^n=

    Text Solution

    |

  3. If absz1=absz2=absz3=1 and z1+z2+z3=0, then z1, z2, z3 are vertices of

    Text Solution

    |

  4. The locus of point z satisfying Re(1/z)=k, where k is a non-zero real ...

    Text Solution

    |

  5. If P represents z=x+iy in the argand plane and abs(z+1-i)=abs(z+i-1) t...

    Text Solution

    |

  6. If alpha/a+beta/b+gamma/c=1+i and a/alpha+b/beta+c/gamma=0, then the v...

    Text Solution

    |

  7. The number of solution of the system of equations Re(z^2)=0, absz=2 is

    Text Solution

    |

  8. z1, z2, z3 are three points lying on the circle absz=1 , maximum value...

    Text Solution

    |

  9. The system of equations abs(z+1-i)=sqrt2 ,absz=3 has

    Text Solution

    |

  10. If z1=a+ib and z2=c+id are complex numbers such that abs(z1)=abs(z2)=1...

    Text Solution

    |

  11. If z1 and z2 be two complex numbers such that abszle1, absz2le1, abs(z...

    Text Solution

    |

  12. If z^4=(z-1)^4, then the roots are represented in the Argand plane by ...

    Text Solution

    |

  13. Let z=1-t+isqrt(t^2+t+2), where t is real parameter. The locus of z in...

    Text Solution

    |

  14. If absz=min{abs(z-1), abs(z+1)}, then

    Text Solution

    |

  15. If z1 and z2 be two complex numbers such that abs(z1+z2)=abs(z1) +abs(...

    Text Solution

    |

  16. if z^2+z+1=0, then the value of (z+1/z)^2+(z^2+1/z^2)^2+(z^3+1/z^3)^2+...

    Text Solution

    |

  17. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

    Text Solution

    |

  18. If z1=a+ib and z2=c+id, a, b, c, dinR, be two complex numbers such tha...

    Text Solution

    |

  19. The sum of the series 2(omega+1)(omega^2+1)+3(2omega+1)(2omega^2+1)+...

    Text Solution

    |

  20. If abs(z-2-2i)=1, then the minimum value of absz is

    Text Solution

    |