Home
Class 12
MATHS
The value of s u msum(n=1)^(13)(i^n+i^(...

The value of `s u msum_(n=1)^(13)(i^n+i^(n+1)),"w h e r e"i=sqrt(-1)"e q u a l s"` `i` (b) `i-1` (c) `-i` (d) `0`

A

i

B

`i-1`

C

`-i`

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 2|50 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

The value of sum_(n=1)^(13) (i^n+i^(n+1)) , where i =sqrt(-1) equals (A) i (B) i-1 (C) -i (D) 0

Prove that z=i^i ,w h e r ei=sqrt(-1) , is purely real.

Find the value of 1+i^(2)+i^(4)+i^(6)+...+i^(2n), where i=sqrt(-1) and n in N.

The value of Sigma_(i=1)^(n)(.^(n+1)C_(i)-.^(n)C_(i)) is equal to

For positive integer n_1,n_2 the value of the expression (1+i)^(n1) +(1+i^3)^(n1) (1+i^5)^(n2) (1+i^7)^(n_20), where i=sqrt-1, is a real number if and only if (a) n_1=n_2+1 (b) n_1=n_2-1 (c) n_1=n_2 (d) n_1 > 0, n_2 > 0

If z=(i)^(i)^(((i)))w h e r e i=sqrt(-1),t h e n|z| is equal to 1 b. e^(-pi//2) c. e^(-pi) d. none of these

The value of ("lim")_(nvec0)[1/n+(e^(1/n))/n+(e^(2/n))/n++(e^((n-1)/n))/n]i s 1 (b) 0 (c) e-1 (d) e+1

The value of int_0^(pi//2)cosx\ e^(sin x)dx\ i s a. 1 b. e-1 c. 0 d. -1

If I_(n)=int_(0)^(pi) e^(x)sin^(n)x " dx then " (I_(3))/(I_(1)) is equal to

Sum of four consecutive powers of i(iota) is zero. i.e., i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0,forall n in I. If sum_(r=-2)^(95)i^(r)+sum_(r=0)^(50)i^(r!)=a+ib, " where " i=sqrt(-1) , the unit digit of a^(2011)+b^(2012) , is

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 1
  1. The value of (1+isqrt(3))/(1-isqrt(3))^(6)+(1-isqrt(3))/(1+isqrt(3))^(...

    Text Solution

    |

  2. The complex numbers sin x + i sin 2x and cos x - i sin 2x are conjug...

    Text Solution

    |

  3. The value of s u msum(n=1)^(13)(i^n+i^(n+1)),"w h e r e"i=sqrt(-1)"e ...

    Text Solution

    |

  4. The value of 1+sum(k=0)^(14) {cos((2k+1)pi)/(15) - isin((2k+1)pi)/(1...

    Text Solution

    |

  5. If z = re^(itheta), then prove that |e^(iz)| = e^(-r sin theta).

    Text Solution

    |

  6. The modulus of sqrt(2i)-sqrt(-2i) is

    Text Solution

    |

  7. Convert of the complex number in the polar form: sqrt()+i

    Text Solution

    |

  8. If -1+sqrt(- 3)=r e^(i \ theta) , then theta is equal to

    Text Solution

    |

  9. The value of (sin frac(pi)(8) + i cos frac(pi)(8))^(8)/((sin frac(pi)(...

    Text Solution

    |

  10. If x=a+b,y=aomega+bomega^2 and z=aomega^2+bomega , prove that xyz=a...

    Text Solution

    |

  11. If z and w are two non-zero complex numbers such that z=-w.

    Text Solution

    |

  12. The square roots of - 2 + 2 sqrt(3)i are :

    Text Solution

    |

  13. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  14. If a = cos 2 alpha + i sin 2 alpha , b= cos 2 beta + i sin 2 beta , ...

    Text Solution

    |

  15. The complex number 2^n/(1+i)^(2n)+(1+i)^(2n)/2^n , n epsilon I is equa...

    Text Solution

    |

  16. If z1=9y^2-4-10 i x ,z2=8y^2-20 i ,w h e r ez1=( z )2, then find z=x+...

    Text Solution

    |

  17. The square roots of 7+24i are

    Text Solution

    |

  18. If omega is a complex cube root of unity then (1-omega+omega^2)(1-omeg...

    Text Solution

    |

  19. If zr=cos(pi/(3r))+isin(pi/(3r)),r=1,2,3, , prove that z1z2z3 zoo=idot

    Text Solution

    |

  20. If omega is a complex cube roots of unity, then find the value of the...

    Text Solution

    |