Home
Class 12
MATHS
If z(1),z(2),z(3) are complex numbers su...

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

A

1

B

less than1

C

greater than 1

D

equal to 13

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMMON ENTRANCE TEST -2016

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos
  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

Similar Questions

Explore conceptually related problems

If z_(1), z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0 and Im(z_(1) z_(2))=0 , then

If |z_(1)|=|z_(2)|=|z_(3)|=1 and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

Let z_(1) and z_(2) be two complex numbers such that |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2) . Then,

If |z_(1)|=|z_(2)|=…... .=|z_(n)|=1 then |z_(1)+z_(2)+ .+z_(n)|=

If z_(1),z_(2) are two complex numbers satisfying the equation : |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then (z_(1))/(z_(2)) is a number which is

If z_(1), z_(2), z_(3) are three complex numbers in A.P., then they lie on

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| , then arg. z_(1)- arg. z_(2) equals :

The number of complex numbers z such that |z-1|=|z+1|=|z-i| equals

If |z_(1)-1|lt2,|z_(2)-2|lt1 , then |z_(1)+z_(2)|

If z_(1),z_(2),z_(3) represent the vertices of an equilateral triangle such that |z_(1)|=|z_(2)|=|z_(3)| , then

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. |(1)/((2+i)^(2))-(1)/((2-i)^(2))|

    Text Solution

    |

  2. If |z(1)|=|z(2)|=…... .=|z(n)|=1 then |z(1)+z(2)+ .+z(n)|=

    Text Solution

    |

  3. If z(1),z(2),z(3) are complex numbers such that : |z(1)|=|z(2)|=|z(3)|...

    Text Solution

    |

  4. The amplitude of (-1)^(5) is

    Text Solution

    |

  5. Find the amplitude of -1/2 + I, sqrt(3)/2

    Text Solution

    |

  6. The amplitude of the conjugate of (1+i)/(1-i) is

    Text Solution

    |

  7. The amplitude of (1+i sqrt(3))/(sqrt(3)+i)

    Text Solution

    |

  8. The amplitude of (-1)^(5) i is

    Text Solution

    |

  9. The amplitude of (1+i)/(1+sqrt(3) i) is

    Text Solution

    |

  10. -1+i sqrt(3)=r e^(i theta) then theta=

    Text Solution

    |

  11. The modulus and amplitude of e^((2 + i pi/3)) is

    Text Solution

    |

  12. If |z(1)|=|z(2)| and arg z(1) + arg z(2)=0 then

    Text Solution

    |

  13. Let z and w be two non-zero complex numbers such that |z|=|w| and arg....

    Text Solution

    |

  14. Let z be a complex number such that |z| = 4 and arg (z) = 5pi//6, then...

    Text Solution

    |

  15. The locus of the point satisfying the condition amp. ((z-1)/(z+1))=(pi...

    Text Solution

    |

  16. The complex number z which satisfies the Equation |(i+z)/(i-z)|=1 lies...

    Text Solution

    |

  17. If z(1) and z(2) are complex number and (z(1))/(z(2)) is purely imagi...

    Text Solution

    |

  18. If |z|=1 and w=(z-1)/(z+1) (where z ne -1), then Re (w) is :

    Text Solution

    |

  19. If the complex number (1-i sin theta)/(1+2 i sin theta) is purely imag...

    Text Solution

    |

  20. The complex numbers z(1), z(2), z(3) are three vertices of a parallelo...

    Text Solution

    |