Home
Class 12
MATHS
The value of i-i^(2)+i^(3)-i^(4)+"……."-i...

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

A

`i`

B

`-i`

C

`1-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

The value of (1 + i)^(4) + (1 -i)^(4) is

i+i^(2)+i^(3)+"………"+i^(101)=

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

The value of (1)/(i)+(1)/(i^2)+(1)/(i^3)+"……"+(1)/(i^(102) is equal to

The value of ((1+sqrt(3)i)/(1 - sqrt(3)i))^(10) is

The value of (1 + i)( 1 + i^(2) ) (1 + i^(3)) (1 + i^(4)) is

(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.

Find the value of 1+i^2+i^4+i^6++i^(2n)

i+i^(2)+i^(3)+i^(4) terms equals

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS
  1. If a and b are the roots of the equation x^(2)+ax+b=0, a ne 0, b ne 0,...

    Text Solution

    |

  2. If x^(2)+px+q=0 has the roots alpha" and "beta, then the value of (alp...

    Text Solution

    |

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

    Text Solution

    |

  4. If the imaginary part of (2+i)/(ai-1) is zero, where a is a real numbe...

    Text Solution

    |

  5. The argument of the complex number ((i)/(2)-(2)/(i)) is equal to

    Text Solution

    |

  6. Let z(1)=3+4i" and "z(2)= -1+2i. Then |z(1)+z(2)|^(2)-2(|z(1)|^(2)+|z(...

    Text Solution

    |

  7. If z(1)" and "z(2) are two non-zero complex numbers such that |z(1)+z(...

    Text Solution

    |

  8. If the equation x^(2)-(2+m)x+(m^(2)-4m+4)=0 in x has equal roots, then...

    Text Solution

    |

  9. The number of integral values of b, for which the equation x^(2)+bx-16...

    Text Solution

    |

  10. If (1+i) is a root of the equation x^(2)-x+(1-i)=0, then the other roo...

    Text Solution

    |

  11. If the roots of the quadratic equation 3x^(2)+2x+a^(2)-a=0 in x are of...

    Text Solution

    |

  12. The number of real roots of the equation |x|^(2)-3|x|+2=0 is

    Text Solution

    |

  13. Let a,b, c be positive real numbers. If (x^(2)-bx)/(ax-c)=(m-1)/(m+1) ...

    Text Solution

    |

  14. The equation k sinx + cos2x= 2k-7 has a solution if

    Text Solution

    |

  15. If z(k)=e^(i thetak) for k= 1, 2, 3, 4 where i^(2)= -1, and if |sum(k=...

    Text Solution

    |

  16. If z=(-1)/(2)+i(sqrt(3))/(2), " then "8+10z+7z^(2) is equal to

    Text Solution

    |

  17. Let z ne 1 be a complex number and let omeg= x+iy, y ne 0. If (omega- ...

    Text Solution

    |

  18. The locus of z such that |(1+iz)/(z+i)|=1 is

    Text Solution

    |

  19. The value of sum(k=0)^(n)(i^(k)+i^(k+1)), where i^(2)= -1, is equal to

    Text Solution

    |

  20. Let z(1)=(2sqrt(3)+ i6sqrt(7))/(6sqrt(7)+ i2sqrt(3))" and "z(2)=(sqrt(...

    Text Solution

    |