Home
Class 12
MATHS
If z= cos.(2pi)/(2n +1) +isin.(2pi)/(2n+...

If `z= cos.(2pi)/(2n +1) +isin.(2pi)/(2n+1), n` is a positive integer, then the equation whose roots are `alpha = z+ z^(3) + ….+ z^(2n-1) and beta = z^2 + z^4 + ….+ z^(2n)`. Is ________________.

Text Solution

Verified by Experts

The correct Answer is:
`4x^2 + 4x + sec^2 (pi)/(2n+1)=0`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|10 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I|50 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise EXERCISE 7|2 Videos

  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If n is a positive integer but not a multiple of 3 and z=-1+i sqrt(3), then (z^(2n)+2^(n)z^(n)+2^(2n)) is equal to

If n is a positive integer greater than unity z is a complex number satisfying the equation z^(n)=(z+1)^(n), then

A complex number z with (Im)(z)=4 and a positive integer n be such that z/(z+n)=4i , then the value of n, is

If z= cos((8pi)/11)+isin((8pi)/11),i=sqrt(-1) then the value of Re(z+z^2+z^3+z^4+z^5) is lambda then 20lambda^2 =

if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10, then

If z + (1)/(z) = 2 cos theta, z in "C then z"^(2n) - 2z^(n) cos (n theta) is equal to

FIITJEE-COMPLEX NUMBER-ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - I
  1. (i) Let z be a non-real complex number lying on the circle |z|=1. Then...

    Text Solution

    |

  2. (i) If 'a' is a complex number such that |a| = 1. Find the values of a...

    Text Solution

    |

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

    Text Solution

    |

  4. If z1, z2 are two complex numbers representing consecutive vertices of...

    Text Solution

    |

  5. The vertices of a triangle in the argand plane are 3+4i, 4+3i and 2 sq...

    Text Solution

    |

  6. If z= cos.(2pi)/(2n +1) +isin.(2pi)/(2n+1), n is a positive integer, t...

    Text Solution

    |

  7. The minimum value of k for which |z-i|^2 + |z-1|^2 =k will represent a...

    Text Solution

    |

  8. if (tanalpha-i(sin ""(alpha)/(2)+cos ""(alpha)/(2)))/(1+2 i sin ""(alp...

    Text Solution

    |

  9. Assuming that log (mn) = log m + logn prove that log x^(n) = n log x, ...

    Text Solution

    |

  10. Show that (1+x)^(n) - nx-1 is divisible by x^(2) for n gt N

    Text Solution

    |

  11. Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is div...

    Text Solution

    |

  12. If n gt 1 and x gt -1, x ne 0, show by the principal of mathematical i...

    Text Solution

    |

  13. Show by using mathematical induction that n^(5) -n is multiple of 5.

    Text Solution

    |

  14. Show that 5^(2n)+1 is divisible by 13 if n is odd. Hence show that 5^9...

    Text Solution

    |

  15. 1.3+2.3^2+3.3^3+..............+n.3^n=((2n-1)3^(n+1)+3)/4

    Text Solution

    |

  16. Show that 2^(2n) + 1 or 2^(2n)-1 is divisible by 5 according as n is o...

    Text Solution

    |

  17. Show that 4.6^(n) +5^(n+1) leaves remainder 9 when divided by 20.

    Text Solution

    |

  18. Show that the expression (n^5)/(5) + (n^3)/(3) + (7n)/(15) is a positi...

    Text Solution

    |

  19. Show by mathematical induction that tan^(-1) .(1)/(3) + tan^(-1). (1)/...

    Text Solution

    |

  20. Given a1=1/2(a0+A/(a0)), a2=1/2(a1+A/(a1)) and a(n+1)=1/2(an+A/(an)) ...

    Text Solution

    |