Home
Class 12
MATHS
The nth roots of -1 can be n terms of a ...

The nth roots of -1 can be n terms of a GP.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

Let a,b,c are respectively the sums of the first n terms, the next n terms and the next n terms of a GP. Show that a,b,c are in GP.

If a be the first term, b be the nth term and P be the product of n terms of a GP then prove that P^2=(ab)^n .

Which of the following can be the nth term of an AP ? 4n+3,3n^(2)+5,n^(3)+1 give reason

Show that the ratio of the sum of first n terms of a G.P. and the sum of (n+1)th term to (2n)th term is (1)/(r^(n)) .

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n+1) to (2n) terms is (1)/(r^(n))

If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms , prove that P^(2)=(ab)^(n) .

If the first and the nth terms of a GP are a and b respectively and if P is the product of the first n terms, then P^(2) is equal to

If the first and the nth terms of a G.P,are a and b ,respectively,and if P is hte product of the first n terms prove that P^(2)=(ab)^(n).

If the sum of the n terms of a G.P. is (3^(n)-1) , then find the sum of the series whose terms are reciprocal of the given G.P..

Square root| cube roots and nth roots of unity and nth roots of z

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If the points P and Q represent the complex numbers z and iz then angl...

    Text Solution

    |

  2. If z1ne-z2 and |z1+z2|=|1/z1 + 1/z2| then :

    Text Solution

    |

  3. Find z, if |(z+1)/(z+i)|=1

    Text Solution

    |

  4. If in the Argand plane z1,z2,z3 and z4 are four points such that |z1|=...

    Text Solution

    |

  5. State true or false: If zne0 then argz+argbarz=0.

    Text Solution

    |

  6. Let z1 and z2 be the roots of z^2+pz+q=0. Then the points represented ...

    Text Solution

    |

  7. If z1,z2 are nonzero complex numbers then |(z1)/(|z1|)+(z2)/(|z2|)|le2...

    Text Solution

    |

  8. The nth roots of -1 can be n terms of a GP.

    Text Solution

    |

  9. In the following, each question has one or more than one correct answe...

    Text Solution

    |

  10. If |z-3i|=3 and amp z in (0, pi/2), then cot(amp z)-theta/z is eqaul ...

    Text Solution

    |

  11. If zne0 then amp z +ampbarz = .

    Text Solution

    |

  12. x+iy=((sqrt3+i)/(1-sqrt3i))^25 then x=, y=.

    Text Solution

    |

  13. If alpha1,alpha2,alpha3,alpha4 be the roots of x^5-1=0 then prove that...

    Text Solution

    |

  14. Consider the quadratic equation az^(2)+bz+c=0 where a,b,c and non-zero...

    Text Solution

    |

  15. If |z^2-4|=2|z| then find the greatest value of |z|.

    Text Solution

    |

  16. If z=2 + t + i sqrt(3-t^2), where t is real and t^2 lt 3, show that t...

    Text Solution

    |

  17. If |z1|=1,|z2|=1 then prove that |z1+z2|^2+|z1-z2|^2 =4.

    Text Solution

    |

  18. z1,z2 are represented by two consecutive vertices of a rhombus, the an...

    Text Solution

    |

  19. Prove that t^(2) + 3t + 3 is a factor of ( t+1)^(n+1)^(n+1) + (t+2)^(2...

    Text Solution

    |

  20. If x^2-x+1 =0 then find the value of (x+1/x)^2+(x^2+1/x^2)^2+(x^3+1/x^...

    Text Solution

    |