Home
Class 11
MATHS
If z1,z2,z3 are three complex numbers an...

If `z_1,z_2,z_3` are three complex numbers and A= `abs[[argz_1,argz_2,argz_3],[argz_2,argz_3,argz_1],[argz_3,argz_1,argz_2]]` then A is divisible by`

A

`arg(z_1+z_2+z_3)`

B

`arg(z_1z_2z_3)`

C

all numbers

D

cannot say

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 are three complex number then prove that z_1Im(barz_2.z_3)+z_2Im(barz_3.z_1)+z_3Im(barz_1.z_2)=0

If z_1 and z_2 are non zero complex numbers such that abs(z_1-z_2)=absz_1+absz_2 then

If z_1,z_2 and z_3,z_4 are two pairs of conjugate complex numbers, then arg(z_1/z_4)+arg(z_2/z_3) equals

If z_1,z_2 are conjugate complex numbers and z_3,z_4 are also conjugate, then arg(z_3/z_2)-arg(z_1/z_4) is equal to

If z_(1), z_(2),z_(3) ,are three complex numbers, prove that z_(1).Im(barz_(2)z_(3))+z_(2).Im(barz_(3)z_(1))+z_(3)Im(bar z_(1)z_(2))=0 where Im(W) = imaginary part of W,where W is a complex number.

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

In complex plane z_(1), z_(2) and z_(3) be three collinear complex numbers, then the value of |(z_(1),barz_(1),1),(z_(2),barz_(2),1),(z_(3), barz_(3),1)| is -

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,z_2 are two non zero complex numbers such that z_1/z_2+z_2/z_1=1 then z_1,z_2 and the origin are

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. z^2+zabsz+absz^2=0 then the locus of z is

    Text Solution

    |

  2. The polynomial x^6+4x^5+3x^4+2x^3+x+1 is divisible by

    Text Solution

    |

  3. If z1,z2,z3 are three complex numbers and A= abs[[argz1,argz2,argz3],...

    Text Solution

    |

  4. If abs(z-i)le2 and z0=5+3i then the maximum value of abs(absiz+z0) is

    Text Solution

    |

  5. If z(Re z ne2) be a complex number such that z^2-4z=absz^2+16/absz^3 t...

    Text Solution

    |

  6. Let z=x+iy be a complex number where x and y are integers then the are...

    Text Solution

    |

  7. If z and w are two nonzero complex numbers such the abs(zw)=1 and arg...

    Text Solution

    |

  8. if log(1/2)(( absz^2+2absz+4)/(2absz^2+1))lt0 then the region traced b...

    Text Solution

    |

  9. If abs(z-2-i)=abszabssin(pi/4-argz) then locus of z is

    Text Solution

    |

  10. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  11. If z=iloge(2-sqrt3) then the value of cosz

    Text Solution

    |

  12. If alpha is the nth root of unity then 1+2alpha+3alpha^2+….to n terms ...

    Text Solution

    |

  13. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

    Text Solution

    |

  14. If alpha=cos((8pi)/11+isin((8pi)/11 then Re(alpha+alpha^2+alpha^3+alph...

    Text Solution

    |

  15. If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus ...

    Text Solution

    |

  16. x^(3m)+x^(3n-1)+x^(3r-2) where m,n,r in N is divisible by

    Text Solution

    |

  17. A fourth root of -1 is

    Text Solution

    |

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

    Text Solution

    |

  19. Let z1 and z2 be complex numbers such that z1 nez2 and absz1=absz2 if ...

    Text Solution

    |

  20. If (x+2)^3-27=0 then a value of x is

    Text Solution

    |