Home
Class 11
MATHS
If i^2=-1, then the sum i+i^2+i^3+... u...

If `i^2=-1,`
then the sum `i+i^2+i^3+...` upto 1000 terms is equal to
a. `1`
b. `-1`
c. `i`
d. `0`

Text Solution

Verified by Experts

Given,
`i^{2}=-1`
`(i+i^{2}+i^{3}+i^{4} ….)` upto `1000` term
`i^{3}=i^{2} cdot i=-i `
...
Promotional Banner

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|117 Videos

  • DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|236 Videos

Similar Questions

Explore conceptually related problems

Write the sum of the series i+i^(2)+i^(3)+ upto 1000 terms.

The sum of the series i+2i^(2)+3i^(3)+... up to 200 terms equals

(1+2i)/(1+3i) is equal to

The sum of i-2-3i+4... up to 100 terms, where i=sqrt(-1) is 50(1-i) b.25i c.25(1+i) d.100(1-i)

If sum_(i=1)^200 sin^-1 x_i=100pi, then sum _(i=1)^200 x_i^2 is equal to

The sequences S=i+2i^(2)+3i^(3)+...... upto 100 terms simplifies to where i=sqrt(-1)

1+i+i^(2)+i^(3) is equal to

1+i+i^(2)+i^(3) is equal to

RD SHARMA-COMPLEX NUMBERS-Solved Examples And Exercises
  1. If z=cos(pi/4)+isin(pi/6) , then a. |z|=1, arg(z)=\ pi/4 b. |z|=1, a...

    Text Solution

    |

  2. The polar form of (i^(25))^3 is

    Text Solution

    |

  3. If i^2=-1, then the sum i+i^2+i^3+... upto 1000 terms is equal to a....

    Text Solution

    |

  4. If z=(-2)/(1+isqrt(3)) , then the value of "arg"(z) is a. pi b. pi/...

    Text Solution

    |

  5. If a=costheta+isintheta, then (1+a)/(1-a) is a. cot(theta/2) b. cot...

    Text Solution

    |

  6. If (1+i)(1+2i)(1+3i)...(1+n i)=a+i b , then 2. 5. 10. 17... (1+n^2\ )...

    Text Solution

    |

  7. If ((a^2+1)^2)/(2a-i)=x+i y , then x^2+y^2 is equal to a. ((a^2+1)^4)/...

    Text Solution

    |

  8. The principal value of the argument of (1+i) is A. pi B. pi/(12) C....

    Text Solution

    |

  9. The least positive integer n such that ((2i)/(1+i))^n is a positive in...

    Text Solution

    |

  10. If z is a non zero complex, number then |(|barz |^2)/(z barz )| is eq...

    Text Solution

    |

  11. If a=1+i , then a^2 equals A. 1-i B. 2i C. (1+i)(1-i) D. (i-1)

    Text Solution

    |

  12. If (x+i y)^(1//3)=a+i b ,\ then\ x/a+y/b is a. 0 b. 1 c. -1 d. none o...

    Text Solution

    |

  13. (sqrt(-2))(sqrt(-3)) is equal to A. sqrt(6) B. -sqrt(6) C. isqrt(6)...

    Text Solution

    |

  14. The argument of (1-isqrt(3))/(1+isqrt(3)) is a. 60^@ b. 120^@ c. 210^@...

    Text Solution

    |

  15. If z=((1+i)/(1-i)), then z^4 equals a. 1 b. -1 c. 0 d non of t...

    Text Solution

    |

  16. If z=(1+2i)/(1-(1-i)^2), then arg(z) equals a. 0 b. pi/2 c. pi ...

    Text Solution

    |

  17. If z=1/((2+3i)^2), then |z| is a. 1/13 b. 1/5 c. 1/12 d. n...

    Text Solution

    |

  18. If z=1/((1-i)(2+3i)), then |z| is a. 1 b. 1/sqrt(26) c. 5/sqrt(...

    Text Solution

    |

  19. If z=1-costheta+isintheta,\ t h e n\ |z| is a. 2sin(theta/2) b. 2cos(t...

    Text Solution

    |

  20. If x+i y=(1+i)(1+2i)(1+3i),\ t h e n\ x^2+y^2 is a. 0 b. 1 c. 100 d. n...

    Text Solution

    |