Home
Class 12
MATHS
If x=p+q,y=pomega+q omega^(2) and z=p om...

If `x=p+q,y=pomega+q omega^(2)` and `z=p omega^(2)+q omega`, where `omega` is a complex cube root of unity, then xyz equals to

A

`p^(3)+q^(3)`

B

`p^(2)-pq+q^(3)`

C

`1+p^(3)+q^(3)`

D

`p^(3)-q^(3)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    SIA PUBLICATION|Exercise PROBLEMS|50 Videos
  • DEFINITE INTEGRALS

    SIA PUBLICATION|Exercise PROBLEMS|42 Videos

Similar Questions

Explore conceptually related problems

If omega is a complex cube root of unity, then (x+1)(x+omega)(x-omega-1)

If 1, omega, omega ^(2) are the cube roots of unity , then w^2=

If |z| =3 , the area of the triangle whose sides are z , omega z and z + omega z (where omega is a complex cube root of unity) is

If omega is a complex cube root of unity , then (x + 1) ( x + omega) ( x- omega - 1) =

If |z|=3 , then area of the triangle whose sides are z , omegaz and z +omegaz (where omega is a complex cube root of unity) is

If omega is a complex cube root of unity and A=[(omega,0),(0, omega)] then A^(100)=

If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(23))pi-(pi)/(4)]

Prove that - omega, " and " - omega^(2) are the roots of z^(2) - z + 1 = 0 , where omega " and " omega^(2) are the complex cube roots of unity .

SIA PUBLICATION-COMPLEX NUMBERS AND DE MOIVRE'S THEOREM-Problems
  1. The number of solutions for z^3+barz=0 is

    Text Solution

    |

  2. The least positive integer n for which (1+i)^(n)=(1-i)^(n). is

    Text Solution

    |

  3. If x=p+q,y=pomega+q omega^(2) and z=p omega^(2)+q omega, where omega i...

    Text Solution

    |

  4. ((1+i)/(1-i))^4+((1-i)/(1+i))^4=

    Text Solution

    |

  5. If a complex number z satisfies |z|^(2)+1=|z^(2)-1|, then the locus of...

    Text Solution

    |

  6. ((1+i)x-i)/(2+i)+((1+2i)y+i)/(2-i)=1rArr(x,y)=

    Text Solution

    |

  7. If a,b,c,d inRR are such that a^2+b^2=4 and c^2+d^2=2 and if (a+ib)^2...

    Text Solution

    |

  8. If alpha is a non real root of the equation x^(6)-1=0 then (alpha^(2)+...

    Text Solution

    |

  9. Let z=a-i/2,a inRR " Then "|i+z|^2-|i-z|^2=

    Text Solution

    |

  10. The locus of the complex number z such that arg ((z-2)/(z+2))=pi/3 is ...

    Text Solution

    |

  11. ((1+i)^2011)/(1-i)^2009=

    Text Solution

    |

  12. z=1+isqrt(3)rArr|Arg z|+|Argbarz|=

    Text Solution

    |

  13. If omega is a complex cube root of unity, then (x+1)(x+omega)(x-omega-...

    Text Solution

    |

  14. The locus of z satisfying the |(x+2i)/(2z+i)| lt 1, inequality where z...

    Text Solution

    |

  15. The points in the set {zinC: Arg " ((z-2)/(Z-6i))=pi/2} lie on the cu...

    Text Solution

    |

  16. If omega is a complex cube root of unity, then sin[(omega^(10)+omega^(...

    Text Solution

    |

  17. If m(1), m(2), m(3) and m(4) respectively denote the moduli of the co...

    Text Solution

    |

  18. The locus of the point z=x+iy satisfying |(z-2i)/(z+2i)|=1 is

    Text Solution

    |

  19. The equation of the locus of 2 such that |(z-i)/(z+i)|=2, where z = x ...

    Text Solution

    |

  20. If alpha1,alpha2,alpha3 respectively denote the moduli of the complex ...

    Text Solution

    |