Home
Class 11
MATHS
If alpha is the nth root of unity then 1...

If `alpha` is the nth root of unity then `1+2alpha+3alpha^2+….`to n terms equal to

A

`(-n)/(1-alpha)^2`

B

`(-n)/(1-alpha)`

C

`(-2n)/(1-alpha)`

D

`(-2n)/(1-alpha)^2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

If alpha Is the fifth root of unity, then, prove that : Log_2|1+alpha+alpha^(2)+alpha^(3)-(1/alpha)|=1

Let alpha ,beta denote the cube roots of unity other than 1 and alpha ne beta let S=underset(n=0)overset302sum(-1)^n(alpha/beta)^n then the value of S is

If alpha_1,alpha_2....alpha_(n-1) are the nth roots of unity then show that (5-alpha_1)(5-alpha_2)(5-alpha_3)...(5-alpha_(n-1))= (5^n-1)/4

If 1, alpha,alpha^2.......alpha^(n-1) are the nth roots of unity then prove that (1-alpha)(1-alpha^2).....(1-alpha^(n-1))=n

If nge3and1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are the n,nth roots of unity, then find value of underset("1"le"i" lt "j" le "n" - "1" )(sum""sum) alpha _ "i" alpha _ "j"

If alpha,beta be the imaginary cube root of unity, then the value of (alpha^4+alpha^2beta^2+beta^4) is

If alpha is a cube root of unity , then find the value of |{:(alpha,alpha^3,alpha^5),(alpha^3,alpha^5,alpha),(alpha^5,alpha,alpha^3):}|

If alpha , beta be the imaginary cube root of unity, then show that alpha^4+beta^4+ alpha^-1beta^-1=0

If 4nalpha=pi , then cotalpha cot2alpha cot3alpha.... cot(2n-1)alpha is equal to

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  2. If z=iloge(2-sqrt3) then the value of cosz

    Text Solution

    |

  3. If alpha is the nth root of unity then 1+2alpha+3alpha^2+….to n terms ...

    Text Solution

    |

  4. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

    Text Solution

    |

  5. If alpha=cos((8pi)/11+isin((8pi)/11 then Re(alpha+alpha^2+alpha^3+alph...

    Text Solution

    |

  6. If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus ...

    Text Solution

    |

  7. x^(3m)+x^(3n-1)+x^(3r-2) where m,n,r in N is divisible by

    Text Solution

    |

  8. A fourth root of -1 is

    Text Solution

    |

  9. If z1=a+ib and z2=c+id are complex numbers such that abs(z1)=abs(z2)=1...

    Text Solution

    |

  10. Let z1 and z2 be complex numbers such that z1 nez2 and absz1=absz2 if ...

    Text Solution

    |

  11. If (x+2)^3-27=0 then a value of x is

    Text Solution

    |

  12. If absomega=1 then the set of points z=omega+1/omega is contained in o...

    Text Solution

    |

  13. If z1 lies on absz=1 and z2 lies on absz=2 then

    Text Solution

    |

  14. IfA(z1),B(z2),C(z3) and D(z4) be the vertices of the square ABCD then

    Text Solution

    |

  15. If z1 and z2 are non zero complex numbers such that abs(z1-z2)=absz1+a...

    Text Solution

    |

  16. The reflection of the complex number (2-i)/(3+i) where (i=sqrt(-1)in t...

    Text Solution

    |

  17. If alpha is a complex constant such that alphaz^2+z+baralpha=0 has are...

    Text Solution

    |

  18. Let A,B,C b ethree sets of complex numbers as defined A={z:Im zge 1} ...

    Text Solution

    |

  19. Let A,B,C b ethree sets of complex numbers as defined A={z:Im zge 1} ...

    Text Solution

    |

  20. Let alpha+ibeta be a complex number and let x+iy=e^(alpha+ibeta) where...

    Text Solution

    |