Home
Class 12
MATHS
If i^(2)= -1, then the sum i+i^(2)+i^(3)...

If `i^(2)= -1`, then the sum `i+i^(2)+i^(3)+"………"` to 1000 terms is equal to

A

`1`

B

`-1`

C

`-i`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
  • BINOMIAL THEOREM

    NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
  • CONIC SECTIONS

    NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If i^(2) = -1 , then i^(1) + i^(2) + i^(3) + ….. + up to 1000 terms is equal to

i+i^(2)+i^(3)+"………"+i^(101)=

The value of i-i^(2)+i^(3)-i^(4)+"……."-i^(100) is equal to

i^(2)+i^(4)+i^(6)+"…………up to "(2k+1) terms, k in N is

If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to

(i) If i= sqrt(-1) , find the sum of i+i^(2)+i^(3)+"…….."i^(99) (ii) Convert (1-i)/(cos ""(pi)/(4)+ isin ""(pi)/(4)) into (a) a+ib (b) polar form.

If (i)^(2) = -1, (i)^(2) + (i)^(4) + (i)^(6) + ...... to (2n + 1) terms =

i^(n) + i^(n+1) + i^(n + 2) + i^(n + 3)

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

Simplify the following: i i^(2)i^(3)……i^(2000)

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If sqrt(a + ib) = x + iy, then possible value of sqrt(a - ib) is

    Text Solution

    |

  2. If (1+i)(1+2i)(1+3i)"……."(1+ni)=a+ib," then "2xx5xx10xx"………"xx(1+n^2) ...

    Text Solution

    |

  3. If i^(2)= -1, then the sum i+i^(2)+i^(3)+"………" to 1000 terms is equal ...

    Text Solution

    |

  4. ((1+sin theta+icos theta)/(1+sin theta - icos theta))^(n)=

    Text Solution

    |

  5. If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b o...

    Text Solution

    |

  6. If Z(1)" and "Z(2) are any two complex numbers, then which one of the ...

    Text Solution

    |

  7. If alpha" and "beta are the roots of the equation x^(2)+2x+4=0, " then...

    Text Solution

    |

  8. If x^(2)+ax+10=0" and "x^(2)+bx-10=0 have a common root, then a^(2)-b^...

    Text Solution

    |

  9. If 2+i is a root of the equation x^(3)-5x^(2)+9x-5=0, then the other r...

    Text Solution

    |

  10. The equation of smallest degree with real co-efficients having 1+i as ...

    Text Solution

    |

  11. The least integer k which makes the roots of the equation x^(2)+5x+k=0...

    Text Solution

    |

  12. If x^(2)px+q=0 is the quadratic equation whose roots are a-2" and "b-2...

    Text Solution

    |

  13. If omega is a complex cube root of unity, then (a+b omega+c omega^(2))...

    Text Solution

    |

  14. If alpha" and "beta are complex cube roots of unity and x=a alpha+ b b...

    Text Solution

    |

  15. If a,b and c are distinct positive real numbers in A.P, then the roots...

    Text Solution

    |

  16. If z(1),z(2)" and "z(3) are any three complex numbers, then the fourth...

    Text Solution

    |

  17. Let a,b be the solutions of x^(2)+px+1=0 and c, d be the solutions of ...

    Text Solution

    |

  18. If alpha" and "beta are the solutions of the quadratic equation ax^(2)...

    Text Solution

    |

  19. A point P which represents a complex number Z moves such that |Z-Z(1)|...

    Text Solution

    |

  20. ((cos theta+isin theta)^4)/((sin theta+icos theta)^5)=?

    Text Solution

    |