Home
Class 12
MATHS
The least positive integer n for which (...

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

A

3

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
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

(sqrt(3)+i)^(6)+(sqrt(3)-i)^(6)=

The least positive integer n, for which ((1+i)^(n))/((1-i)^(n-2)) is positive is

The smallest positive integer n for which (1+i sqrt(3))^(n / 2) is real is

If n is a positive integer, then: (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is:

The smallest positive integer for which (1 + i)^(2n)=(1 -l)^(2n) is

The smallest positive integer n for which (1+i)^(n) is purely imaginary is

Show that there is no positive integer, n for which sqrt(n-1) + sqrt(n+1) is rational .

If P(n): 2^(n)ltn! Then the smallest positive integer for which P(n) is true, is

If P(n):2^(n) lt n! Then the smallest positive integer for which P(n) is true if

(1+i sqrt(3))^(5)+(1-i sqrt(3))^(5)=

HIMALAYA PUBLICATION-COMPLEX NUMBERS-QUESTION BANK
  1. If arg (z)lttheta, then arg (-z)-arg (z)=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. 1+i^(2)+i^(4)+i^(6)+... .+i^(2 n)=

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. The real value of thetafor which the expression is (1+icos theta)/(1...

    Text Solution

    |