Home
Class 12
MATHS
Find the value of 1+i^2+i^4+i^6++i^(2n)...

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

Text Solution

Verified by Experts

`S = 1 + i^(2) + i^(4) + …….+ i^(2n) = 1 - 1 + 1-1 +…….+ (-1)^(n)`
Obsviously it depends on n . Hence,it cannot be determined unless n is known.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.2|9 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

Find the value of ( i^2 + i^4 + i^6 + i^7 ) / ( 1 + i^2 + i^3 ) is ( a ) 1 - i ( b ) 1 + i ( c ) 2 - i ( d ) 2 + i

Find the value of i^4 + i^5 + i^6 + i^7

Find the value of : i^4 + i^5 + i^6 + i^7

Find the value of : i^4 + i^5 + i^6 + i^7

Find the value of 1+i^(2)+i^(4)+i^(6)+i^(8)+...+i^(24)

Find the value of 1+i^(2)+i^(4)+i^(6)+i^(8)+...+i^(24)

Find the value of ( i^2 + n ) ( i^2 + n - 1 ) ( i^2 + n - 2 ) .......( i^2 + 1 )

Find the value of 1+i^2+i^4+i^6+i^8+.....+i^20

Find the value of ( i^2 + 1 ) times ( i^2 + 2 ) times ( i^2 + 3 ) ------ ( i^2 + n )

CENGAGE-COMPLEX NUMBERS-Examples
  1. Evaluate : (i) i^(135) (ii) i^((1)/(47) (iii) (-sqrt(-1))^(4n...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisibl...

    Text Solution

    |

  5. Solve: i x^2-3x-2i=0,

    Text Solution

    |

  6. If z=4+isqrt(7) , then find the value of z^3-4z^2-9z+91.

    Text Solution

    |

  7. Express each of the following in the standerd from a + ib (i) (5+...

    Text Solution

    |

  8. The root of the equation 2(1 + i) x^2-4(2-i) x-5-3 i = 0, where i = sq...

    Text Solution

    |

  9. Find the value of (1+ i)^(6) + (1-i)^(6)

    Text Solution

    |

  10. If ((1+i)/(1-i))^m=1, then find the least positive integral value of m...

    Text Solution

    |

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

    Text Solution

    |

  12. Find the value of theta if (3+2isintheta)/(1-2isintheta) is purely rea...

    Text Solution

    |

  13. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

    Text Solution

    |

  14. If z is a complex number such that |z - barz| +|z + barz| = 4 then fi...

    Text Solution

    |

  15. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

    Text Solution

    |

  16. If z = x + iy lies in the third quadrant, then prove that (barz)/(z) ...

    Text Solution

    |

  17. Prove that (sqrt(3)/(2) +(i)/(2))^(5) + (sqrt(3)/(2) -(i)/(2))^(5) is...

    Text Solution

    |

  18. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  19. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

    Text Solution

    |

  20. Find real values of x and y for which the complex numbers -3+i x^2y an...

    Text Solution

    |