Home
Class 12
MATHS
If n in N , then find the value of i^n+...

If `n in N ,` then find the value of `i^n+i^(n+1)+i^(n+2)+i^(n+3)dot`

A

1

B

i

C

`i^(n)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=i^(n)(1+i+i^(2)+i^(3))=i^(n)(1+i-1-i)=0`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|141 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|15 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

Similar Questions

Explore conceptually related problems

If n in NN , then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) .

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

If Sigma_( i = 1)^( 2n) sin^(-1) x_(i) = n pi , then find the value of Sigma_( i = 1)^( 2n) x_(i) .

If Sigma_(i=1)^(2n) cos^(-1) x_(i) = 0 ,then find the value of Sigma_(i=1)^(2n) x_(i)

For a positive integer n , find the value of (1-i)^(n) (1 - 1/i)^(n)

For a positive integer n , find the value of (1-i)^n(1-1/i)^ndot

For a positive integer n , find the value of ( 1-i)^n(1-1/i)^ndot

Find the value of sumsum_(0leilejlt=n)(i+j)(nC_i+n C_j)dot

If n is any positive integer, write the value of (i^(4n+1)-i^(4n-1))/2 .

OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Chapter Test
  1. If n in N , then find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3)dot

    Text Solution

    |

  2. The locus of the center of a circle which touches the circles |z-z1|=a...

    Text Solution

    |

  3. Prove that for positive integers n(1) and n(2), the value of express...

    Text Solution

    |

  4. The value of abs(sqrt( 2i) - sqrt(2i)) is :

    Text Solution

    |

  5. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

    Text Solution

    |

  6. The value of ((1+ i sqrt(3))/(1-isqrt(3)))+ ((1-isqrt(3))/(1+isqrt(3)...

    Text Solution

    |

  7. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

    Text Solution

    |

  8. If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...

    Text Solution

    |

  9. Find the sum 1xx(2-omega)xx(2-omega^(2))+2xx(-3-omega)xx(3-omega^(2))+...

    Text Solution

    |

  10. The value of the expression (1+(1)/(omega))+(1+(1)/(omega^(2)))+(2+(1)...

    Text Solution

    |

  11. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

    Text Solution

    |

  12. The expression (1+i)^(n1)+(1+i^(3))^(n2) is real iff

    Text Solution

    |

  13. If |{:(6i,3i,1),(4,3i,-1),(20,3,i):}|=x+iy, then (x, y) is equal to

    Text Solution

    |

  14. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

  15. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

  16. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

    Text Solution

    |

  17. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

    Text Solution

    |

  18. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

    Text Solution

    |

  19. If Re((z+4)/(2z-1)) = 1/2 then z is represented by a point lying on

    Text Solution

    |

  20. The vertices of a square are z(1),z(2),z(3) and z(4) taken in the anti...

    Text Solution

    |

  21. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |