Home
Class 12
MATHS
The conjugate of i^(13) + i^(14) + i^(15...

The conjugate of `i^(13) + i^(14) + i^(15) + i^(16)` is …………

A

1

B

`-1`

C

`0`

D

`-i`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.1|6 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.2|3 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.9|25 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    FULL MARKS|Exercise Additional Questions Solved|29 Videos

Similar Questions

Explore conceptually related problems

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

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

i^(1948)-i^(-1869)

The value of sum_(i=1)^(13) (n^(n) + i^(n-1)) is

(1+i)^(16)+(1-i)^(16) equals

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

The conjugate of a complex number is (1)/(i-1) . Then that complex number is

Simplify the following : (i) i^7 " " (ii) i^(1729) " " (iii) i^(-1924) + i^(2018) " " (iv) sum_(n=1)^(102) i^(n) " " (v) i i^2 i^3 …..i^(40)

FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
  1. ((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

    Text Solution

    |

  2. If ((1 + i)/(1 - i))^(3) - ((1 - i)/(1 + i))^(3) = x + iy then (x, y) ...

    Text Solution

    |

  3. Evaluate i^(60)

    Text Solution

    |

  4. Fill in the blanks of the following : For any two complex numbers z1...

    Text Solution

    |

  5. Multiplicative inverse of 1 + i is ………..

    Text Solution

    |

  6. arg(z) + arg(barz) (z != 0) is ………..

    Text Solution

    |

  7. If |z| = 4 and arg(z) = (5pi)/6, then z = …………..

    Text Solution

    |

  8. If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c...

    Text Solution

    |

  9. If p +iq = (a + ib)/(a - ib) then p^2 + q^2 = …………

    Text Solution

    |

  10. Evaluate i^(78)

    Text Solution

    |

  11. If a =cos alpha - i sin alpha, b= cos beta - i sin beta, c = cos gamma...

    Text Solution

    |

  12. If z(1)=4+5i and z(2)=-3+2i that (z(1))/(z(2)) is :

    Text Solution

    |

  13. The conjugate of i^(13) + i^(14) + i^(15) + i^(16) is …………

    Text Solution

    |

  14. If -i + 2 is one root of the equation ax^2 - bx + c = 0, then the othe...

    Text Solution

    |

  15. The equation having 4 + 3i and 4 - 3i as root is ………..

    Text Solution

    |

  16. If 2−i is one root of the equation ax^2+bx+c=0, and a,b,c are rational...

    Text Solution

    |

  17. If -i+3 is a root of x^(2)-6x+k=0. Then the value of k is :

    Text Solution

    |

  18. If omega is a cube root of unity, then the value of (1 - omega + omega...

    Text Solution

    |

  19. If omega is the cube root of unity, then then value of (1 - omega) (1 ...

    Text Solution

    |

  20. If (z - 1)/(z + 1) is purely imaginary, then |z| is

    Text Solution

    |