Home
Class 12
MATHS
If alpha is a non-real fifth root of uni...

If alpha is a non-real fifth root of unity, then `3^(|1+alpha+a^(2)+a^(-2)-a^(-1) |)=`

A

9

B

1

C

`(11)/(3)`

D

`(1)/(9)`

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 alpha is a non-real fourth roots of unity, then the values of alpha^(4 n-1)+alpha^(4 n-2)+alpha^(4 n-3), n in N is

If alpha is an imaginary fifth root of unity then log _(2)|1+alpha+alpha^(2)+alpha^(3)-(1)/(alpha)|=

If alpha and beta are non real cube roots of unity then alpha beta+alpha^(5)+beta^(5)=

If omega is a non real cube root of unity then (a+b)(a+b omega)(a+b omega^(2)) is

If alpha and beta are the roots of x^(2)+x+1=0 , then alpha^(16)+beta^(16)=

If i=sqrt(-1), omega is a non real cube root of unity then ((1+i)^(2 n)-(1-i)^(2 n))/((1+omega-omega^(2))(1-omega+omega^(2)))=

If alpha is the nth root of unity then 1+2alpha+3alpha^(2)+ ............to n terms is equal to

If alpha and beta are the roots of x^(2) - ax + b^(2) = 0, then alpha^(2) + beta^(2) is equal to :

If alpha and beta are the roots of x^(2)-ax+b^(2)=0 , then alpha^(2) +beta^(2) is equal to_______

If alpha and beta are the root of the equation x^(2)-x+1=0 then alpha^(2009)+beta^(2009)=

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If |z|=k and w=(z-k)/(z+k), then Re (w)=

    Text Solution

    |

  2. If z is a complex number satisfying z^(4)+z^(3)+2 z^(2)+z+1=0 then |z|...

    Text Solution

    |

  3. If alpha is a non-real fifth root of unity, then 3^(|1+alpha+a^(2)+a^(...

    Text Solution

    |

  4. If alpha is a non-real fourth roots of unity, then the values of alpha...

    Text Solution

    |

  5. If x^(2)-x+1=0 then the value of sum(n=1)^(5)(x^(n)+(1)/(x^(n)))^(2) ...

    Text Solution

    |

  6. If arg (z)lttheta, then arg (-z)-arg (z)=

    Text Solution

    |

  7. If (sqrt(3)-i)^(n)=2^(n), n in Z, then n is a multiple of

    Text Solution

    |

  8. The least positive integer n for which (sqrt(3)+i)^(n)=(sqrt(3)-i)^(n)...

    Text Solution

    |

  9. If w is a complex cube roots of unity, then arg (i w)+arg (i w^(2))=

    Text Solution

    |

  10. If z(2-2 sqrt(3) i)^(2)=i(sqrt(3)+i)^(4) then arg z=

    Text Solution

    |

  11. If ((3)/(2)+(i sqrt(3))/(2))^(28)=3^(14)(x+i y) then (x, y)= (where x ...

    Text Solution

    |

  12. If 1, alpha(1), alpha(2), …., alpha(n-1) are the n^(text (th ) roots o...

    Text Solution

    |

  13. The argument of (1-i sqrt(3))/(1+i sqrt(3))=

    Text Solution

    |

  14. Let z(1) and z(2) be two complex numbers such that |z(1)+z(2)|^(2)=|z(...

    Text Solution

    |

  15. If z is purely imaginary then and Im(z)gt0, then amp(z)=

    Text Solution

    |

  16. If n is an odd integer, then (1+i)^(6 n)+(1-i)^(6 n) is equal to

    Text Solution

    |

  17. The amplitude of "sin"(pi)/(5)+i(1-"cos"(pi)/(5)) is

    Text Solution

    |

  18. Number of solutions of the equation z^(2)+|z|^(2)=0 is

    Text Solution

    |

  19. The equation |z+1-i|=|z-1+i| represents a

    Text Solution

    |

  20. The area of the triangle on the complex plane formed by the complex nu...

    Text Solution

    |