Home
Class 12
MATHS
If alpha is a complex number such that a...

If `alpha` is a complex number such that `alpha^(2) - alpha + 1 = 0` , then `alpha^(2011)` =

A

1

B

`-alpha`

C

`alpha^(2)`

D

`alpha`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • KARNATAKA CET 2010

    KCET PREVIOUS YEAR PAPERS|Exercise Mathematics|60 Videos

  • KARNATAKA CET 2013

    KCET PREVIOUS YEAR PAPERS|Exercise Mathematics|60 Videos

Similar Questions

Explore conceptually related problems

If alpha is a complex number such that alpha^(2)+alpha+1=0 then alpha^(31) is

If alpha is a number satisfying the equation alpha^(2)+alpha+1=0 then alpha^(31) is equal to

If alpha,beta are two complex numbers such that |alpha|=1 , |beta|=1 , then the expression |(beta-alpha)/(1-baralphabeta)| equals

Let p and q be real number such that p ne 0 , p^(3) ne q and p^(3) ne -q . If alpha and beta non- zero complex number satifying alpha+ beta= -p and alpha^(3) + beta^(3) =q then a quadratic equation having (alpha)/(beta) and (beta) /(alpha) as its roots is :

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

Let alpha and beta be two distinct complex numbers, such that abs(alpha)=abs(beta) . If real part of alpha is positive and imaginary part of beta is negative, then the complex number (alpha+beta)//(alpha-beta) may be

If alpha, beta are the roots of ax^(2) - 26x + c = 0 , then alpha^(3) beta^(3) + alpha^(2) beta^(3) + alpha^(3) beta^(2) equals :

If alpha and beta are the roots of the equation x^(2) - p(x + 1) - q = 0 , then the value of : (alpha^(2) + 2 alpha + 1)/(alpha^(2)+ 2 alpha + q) + (beta^(2) + 2 beta + 1)/(beta^(2) + 2 beta + q) is :

If alpha , beta are the roots of the equation : x^(2) + x sqrt(alpha) + beta = 0 , then the values of alpha and beta are :

The expression tan ^(2) alpha+cot ^(2) alpha is

KCET PREVIOUS YEAR PAPERS-KARNATAKA CET 2012-MATHEMATICS
  1. Which of the following is false ?

    Text Solution

    |

  2. 2 cos^(-1) x = sin^(-1) (2x sqrt(1 - x^(2))) is valid for all values o...

    Text Solution

    |

  3. If alpha is a complex number such that alpha^(2) - alpha + 1 = 0 , the...

    Text Solution

    |

  4. If cos alpha + 2 cos beta + 3 cos gamma = 0 , sin alpha + 2 sin beta +...

    Text Solution

    |

  5. If the conjugate of (x + iy) ( 1 - 2i) is 1 + i, then

    Text Solution

    |

  6. If the straight line 3x + 4y = k touches the circle x^(2) + y^(2) = 1...

    Text Solution

    |

  7. The locus of the point of intersection of perpendicular tangents to th...

    Text Solution

    |

  8. If m sin^(-1) x = log (e) y , then (1 - x^(2)) y'' - xy' =

    Text Solution

    |

  9. If y = e^(log(e) [1 + x + x^(2) + …]) , then (dy)/(dx) =

    Text Solution

    |

  10. The length of the sub - tangent to the curve x^(m)y^(n) = a^(m+n) at a...

    Text Solution

    |

  11. If a ball is thrown vertically upward and the height 's' reached in ti...

    Text Solution

    |

  12. The sum of two positive numbers is given . If the sum of their cubes i...

    Text Solution

    |

  13. int(pi//6)^(pi//3) (sin^(3) x)/(sin^(3) x + cos^(3) x) dx=

    Text Solution

    |

  14. Lt(x to 0) (x 2^(x) - x)/(1 - cos x ) =

    Text Solution

    |

  15. (3x + 1)/(( x- 1) (x - 3)) = (A)/(x - 1) + (B)/(x - 3) , then sin^(-1)...

    Text Solution

    |

  16. If alpha , beta , gamma are the roots of the equation x^(3) + 4x + 2 =...

    Text Solution

    |

  17. The value of ""^(10) C(2) + ""^(10) C(3) + … + ""^(10) C(9) is

    Text Solution

    |

  18. p to - q can also be written as

    Text Solution

    |

  19. If f : R to R is defined by f (x) = 2x + 3 , then f^(-1) x

    Text Solution

    |

  20. (sin 70^(@) + cos 40^(@))/(cos 70^(@) + sin 40^(@)) =

    Text Solution

    |