Home
Class 12
MATHS
For any integer k , let alphak=cos(kpi)/...

For any integer `k ,` let `alpha_k=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt(-1)dot` Value of the expression `(sumk=1 12|alpha_(k+1)-alpha_k|)/(sumk=1 3|alpha_(4k-1)-alpha_(4k-2)|)` is

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|12 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

For any integer k, let alpha_(k)=cos((k pi)/(7))+i sin((k pi)/(7)), wherei =sqrt(-1) Value of the expression (sum_(k=1)^(12)| alpha_(k+1)-alpha_(k)|)/(sum_(k=1)^(3)| alpha_(4k-1)-alpha_(4k-2)|) is

Solve the equation (1+k)cosxcos(2x-alpha)=(1+kcos2x)cos(x-alpha)

If an angle alpha is divided into two parts A&B such that A-B=x and tan A:tan B=k:1 Then the value of sin x is (A) (k+1)/(k-1)sin alpha (k)/(k+1)sin alpha (C) (k-1)/(k+1)sin alpha (D) tan alpha

If sin theta=k sin(theta+2 alpha) prove that tan(theta+alpha)=(1+k)/(1-k)tan alpha

If k>1, and the determinant of the matrix A^(2)=[[k,k alpha,alpha0,alpha,k alpha0,0,k]] is (:k^(2) then | alpha|=

If alpha_(1),alpha_(2),alpha_(3),.........,alpha_(n) are the roots of f(x)=0 then the equation whose roots (alpha_(1))/(K),(alpha_(2))/(K),(alpha_(3))/(K),.........(alpha_(n))/(K) is where , K!=0

If alpha,beta are the zeros of the polynomial x^(2)-(k+6)x+2(2k-1)* Find k if alpha+beta=(1)/(2)(alpha*beta)

If alpha_r=(cos2rpi+isin2rpi)^(1/10) , then |(alpha_1, alpha_2, alpha_4),(alpha_2, alpha_3, alpha_5),(alpha_3, alpha_4, alpha_6)|= (A) alpha_5 (B) alpha_7 (C) 0 (D) none of these

If k>1, and the determinant of the matrix A^(2)=[[k,k alpha,alpha0,alpha,k alpha0,0,k]] is k^(2) then | alpha|=

ARIHANT MATHS-COMPLEX NUMBERS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If z is any complex number satisfying abs(z-3-2i) le 2, where i=sqrt(-...

    Text Solution

    |

  2. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

    Text Solution

    |

  3. The maximum value of |a r g(1/(1-z))|for|z|=1,z!=1 is given by.

    Text Solution

    |

  4. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |

  5. Let alpha and beta be real numbers and z be a complex number. If z^(2...

    Text Solution

    |

  6. If omega(ne 1) be a cube root of unity and (1+omega)^(7)=A+Bomega, the...

    Text Solution

    |

  7. Let z be a complex number such that the imaginary part of z is nonzero...

    Text Solution

    |

  8. If z ne 1 and (z^(2))/(z-1) is real, the point represented by the comp...

    Text Solution

    |

  9. If z is a complex number of unit modulus and argument theta, then arg(...

    Text Solution

    |

  10. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2(y-y0)^2=...

    Text Solution

    |

  11. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

    Text Solution

    |

  12. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  13. Let S=S1 nn S2 nn S3, where s1={z in C :|z|<4}, S2={z in C :ln[(z-...

    Text Solution

    |

  14. If z is a complex number such that |z|>=2 then the minimum value of |z...

    Text Solution

    |

  15. A complex number z is said to be unimodular if abs(z)=1. Suppose z(1) ...

    Text Solution

    |

  16. Let omega ne 1 be a complex cube root of unity. If (3-3omega+2omega^(2...

    Text Solution

    |

  17. For any integer k , let alphak=cos(kpi)/7+isin(kpi)/7,w h e r e i=sqrt...

    Text Solution

    |

  18. A value of theta for which (2+3isintheta)/(1-2isintheta) is purely ima...

    Text Solution

    |

  19. Let 0 ne a, 0 ne b in R. Suppose S={z in C, z=1/(a+ibt)t in R, t ne ...

    Text Solution

    |

  20. Let omega be a complex number such that 2omega+1=z where z=sqrt(-3). I...

    Text Solution

    |