Home
Class 12
MATHS
Let zk be the roots of the equation (z+1...

Let `z_k` be the roots of the equation `(z+1)^7+z^7=0`, then `sum _(k=0)^6 Re(z_k)` is `-k/2`, then `k` is-------------

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If z_(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0 , then sum_(r=0)^(6)"Re"(z_(r))=

The number of real roots of equation sum_(k=1)^(oo)(x-k^(k))^(7)=0;(n>5)

Let Z=re^(itheta)(r gt 0 and pi lt theta lt 3pi) is a root of the equation Z^(8)-Z^(7)+Z^(6)-Z^(5)+Z^(4)-Z^(3)+Z^(2)-Z+1=0 . the sum of all values of theta is kpi . Then k is equal to

Let alpha, beta be ral roots of the quadratic equation x ^(2)+kx+ (k^(2) +2k-4) =0, then the minimum value of alpha ^(z)+beta ^(z) is equal to :

Let z be a non - real complex number which satisfies the equation z^(23) = 1 . Then the value of sum_(22)^(k = 1 ) (1)/(1 + z ^( 8k) + z ^( 16k ))

If z-(1)/(z)=i then z^(2005)+(1)/(z^(2005))=+-sqrt(k) then k is

RESONANCE DPP-JEE MAINS-All Questions
  1. If H is the orthocenter of DeltaABC and if AH = x, BH = y, CH = z, t...

    Text Solution

    |

  2. C1 and C2 are fixed circles of radii r1 and r2 touches each other ext...

    Text Solution

    |

  3. Let zk be the roots of the equation (z+1)^7+z^7=0, then sum (k=0)^6 Re...

    Text Solution

    |

  4. Find the equations of the sides of the triangle having (3, - 1) as a v...

    Text Solution

    |

  5. The equation of the circle which passes through the point A(0, 5) and ...

    Text Solution

    |

  6. One diagonal of a square is the portion of the line sqrt(3)x+y=2sqrt(3...

    Text Solution

    |

  7. Three vertices of a parallelogram are (1, 1), (2, 4)  and (3,5), then ...

    Text Solution

    |

  8. If the vectors 2a hat i+b hat j+c hat k ,b hat i+c hat j+2a hat ka n d...

    Text Solution

    |

  9. In a triangle A B C , right angled at A , on the leg A C as diameter, ...

    Text Solution

    |

  10. Let a, b, c be any real numbers. Suppose that there are real number...

    Text Solution

    |

  11. underset(x to oo)lim(overset(2x)underset(0)intte^(t^(2))dt)/(e^(4x^(2)...

    Text Solution

    |

  12. ("lim")(x→oo)((a x+3)/(b x+2))^(b x) is equal to (a and b are positive...

    Text Solution

    |

  13. a, b, c are sides of a triangle and a, b, c are in GP If log a- log ...

    Text Solution

    |

  14. The equation 2log(x+3)="log"(alphax) has only one solution if alpha=12...

    Text Solution

    |

  15. If x^2+2a x+a<0AAx in [1,2], the find the values of adot

    Text Solution

    |

  16. If f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well...

    Text Solution

    |

  17. A box contains 1 black and 1 white ball. A ball is drawn randomly and ...

    Text Solution

    |

  18. On a normal standard die one of the 21 dots from any one of the six...

    Text Solution

    |

  19. Number of all four digit numbers having different digits formed of the...

    Text Solution

    |

  20. In how many ways 3 boys and 15 girls can sits together in a row such ...

    Text Solution

    |