Home
Class 11
MATHS
For any integer k let alphak=cos((kpi)/7...

For any integer k let `alpha_k=cos((kpi)/7)+isin((kpi)/7)` where `i=sqrt(-1)` the value of expression `(sum_(k=1)^(12) abs(alpha_(k+1)-alpha_k))/(sum_(k=1)^3 abs((alpha_(4k-1)-alpha_(4k-2))`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

For any integer K , let alpha_(k)=cos((kpi)/(7))+isin((kpi)/(7))," where " i=sqrt(-1) The value of the expression (sum_(k=1)^(12)|alpha_(k+1)-alpha_(k)|)/(sum_(k=1)^(3)|alpha_(4k-1)-alpha_(4k-2)|)

The value of cot(sum_(n=1)^(23)cot^-1(1+sum_(k=1)^n2k)) is

sum_(k=1)^ook(1-1/n)^(k-1) =?

Evaluate sum_(k=1)^11(2+3^k)

The value of cot {sum_(n=1)^(23)cot^(-1)""(1+sum_(k-1)^(n)2k)} is

Find the sum of the series sum_(k=1)^(360)(1/(ksqrt(k+1)+(k+1)sqrt(k)))

Find the largest real value of x such that sum_(k=0)^4((3^(4-k))/((4-k)!))((x^k)/(k !))=(32)/3 .

Prove that: sum_(k=1)^(100)sin(k x)cos(101-k)x=50"sin"(101 x)

If k, 2(k+1), 3(k+1) are in GP, Then find the value of k.

Value of sum_(m=1)^(n)(sum_(k=1)^(m)(sum_(p=k)^(m)"^(n)C_(m)*^(m)C_(p)*^(p)C_(k)))=

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x ,y in R satify the equation x^2+y^2-4x-2y+5=0, then the value of...

    Text Solution

    |

  2. If |z-i R e(z)|=|z-I m(z)| , then prove that z , lies on the bisectors...

    Text Solution

    |

  3. For any integer k let alphak=cos((kpi)/7)+isin((kpi)/7) where i=sqrt(-...

    Text Solution

    |

  4. If x=1+1/(3+1/(2+1/(3+1/(2)))) a 52/2 b. 55/71 c. 60/52 d....

    Text Solution

    |

  5. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

    Text Solution

    |

  6. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

    Text Solution

    |

  7. Find the values of a for which all the roots of the euation x^4-4x^3-8...

    Text Solution

    |

  8. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

    Text Solution

    |

  9. Let |(( bar z 1)-2( bar z 2))//(2-z1( bar z 2))|=1 and |z2|!=1,where z...

    Text Solution

    |

  10. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a)3 ...

    Text Solution

    |

  11. Let 1,w,w^2 be the cube root of unity. The least possible degree of a ...

    Text Solution

    |

  12. If z1a n dz2 are complex numbers and u=sqrt(z1z2) , then prove that |z...

    Text Solution

    |

  13. The least value of the expression x^2+4y^2+3z^2-2x-12 y-6z+14 is a....

    Text Solution

    |

  14. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

    Text Solution

    |

  15. If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus o...

    Text Solution

    |

  16. If x=2+2^(2//3)+2^(1//3) , then the value of x^3-6x^2+6x is (a)3 ...

    Text Solution

    |

  17. Let z=x+i ydot Then find the locus of P(z) such that (1+ bar z )/z ...

    Text Solution

    |

  18. (costheta + isintheta)^4/(sintheta + icostheta)^5 is equal to.

    Text Solution

    |

  19. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  20. Identify locus z if R e(z+1)=|z-1|

    Text Solution

    |