Home
Class 12
MATHS
If (sqrt(3)-i)^(n)=2^(n), n in Z, then n...

If `(sqrt(3)-i)^(n)=2^(n)`, n in Z, then n is a multiple of

A

6

B

10

C

9

D

12

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMMON ENTRANCE TEST -2016

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|60 Videos

  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

Similar Questions

Explore conceptually related problems

n(n+1)(n+5) is a multiple 3.

(1+i)^(2 n)+(1-i)^(2 n), n in z is

41^(n)-14^(n) is multiple of 27.

If ((1+i sqrt(3))/(1-i sqrt(3)))^(n) is an integer, then n=

Using mathematical induction , show that n(n+1)(n+5) is a multiple of 3 .

If I_(n) = int x^(n)e^(x) dx where n inN , then I_(n) + nI_(n-1) =

If the second term in the expansion ((a)^(1/13)+(a)/(sqrt(a^(-1))))^(n) is 14 a^(5 / 2) then the value of (n C_(3))/(n C_(2)) is

Prove that by using the principle of mathematical induction for all n in N : 41^(n)-14^(n) is multiple of 27

The functon f: N rarr N , defined by f(n)=2n+3 , for all n in N , is (here N is the set of natural numbers)

Which of the following is a subgroup of the group G = {2^(n)| n in N } under multiplication ?

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If x^(2)-x+1=0 then the value of sum(n=1)^(5)(x^(n)+(1)/(x^(n)))^(2) ...

    Text Solution

    |

  2. If arg (z)lttheta, then arg (-z)-arg (z)=

    Text Solution

    |

  3. If (sqrt(3)-i)^(n)=2^(n), n in Z, then n is a multiple of

    Text Solution

    |

  4. The least positive integer n for which (sqrt(3)+i)^(n)=(sqrt(3)-i)^(n)...

    Text Solution

    |

  5. If w is a complex cube roots of unity, then arg (i w)+arg (i w^(2))=

    Text Solution

    |

  6. If z(2-2 sqrt(3) i)^(2)=i(sqrt(3)+i)^(4) then arg z=

    Text Solution

    |

  7. If ((3)/(2)+(i sqrt(3))/(2))^(28)=3^(14)(x+i y) then (x, y)= (where x ...

    Text Solution

    |

  8. If 1, alpha(1), alpha(2), …., alpha(n-1) are the n^(text (th ) roots o...

    Text Solution

    |

  9. The argument of (1-i sqrt(3))/(1+i sqrt(3))=

    Text Solution

    |

  10. Let z(1) and z(2) be two complex numbers such that |z(1)+z(2)|^(2)=|z(...

    Text Solution

    |

  11. If z is purely imaginary then and Im(z)gt0, then amp(z)=

    Text Solution

    |

  12. If n is an odd integer, then (1+i)^(6 n)+(1-i)^(6 n) is equal to

    Text Solution

    |

  13. The amplitude of "sin"(pi)/(5)+i(1-"cos"(pi)/(5)) is

    Text Solution

    |

  14. Number of solutions of the equation z^(2)+|z|^(2)=0 is

    Text Solution

    |

  15. The equation |z+1-i|=|z-1+i| represents a

    Text Solution

    |

  16. The area of the triangle on the complex plane formed by the complex nu...

    Text Solution

    |

  17. If the complex number z=x+ iy satisfies the condition |z+1|=1, then z ...

    Text Solution

    |

  18. 1+i^(2)+i^(4)+i^(6)+... .+i^(2 n)=

    Text Solution

    |

  19. If f(z)=(7-z)/(1-z^(2)), where z=1+2 i, then |f(z)| is

    Text Solution

    |

  20. The value of arg (x) when xlt0 is

    Text Solution

    |