Home
Class 12
MATHS
Simplify (si n (pi)/6 + i co s (pi)/6)^(...

Simplify `(si n (pi)/6 + i co s (pi)/6)^(18)`.

Text Solution

Verified by Experts

The correct Answer is:
1
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise ADDITIONAL QUESTIONS SOLVED|59 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.1|6 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

Simplify : ("sin"pi/6+i"cos"pi/6)^(08) .

Find the value of ((1 + sin"" (pi)/(10) + i cos"" (pi)/(10))/(1 + sin"" (pi)/(10) - i cos"" (pi)/(10)))^(10) .

Simplify sin^(-1) (sin . pi/6)

Simplify tan^(-1) (tan. (5pi)/6)

Find cos^(-1) (cos (-pi/6))

Simplify (I ) cos ^(-1) ( cos ((13 pi )/(3))) (ii ) tan^(-1) ( tan ((3pi)/(4))) (iii ) sec^(-1) ( sec ((5pi )/(3))) (iv ) sin^(-1) [ sin 10 ]

Find the rectangular form of the complex numbers. (cos" " (pi)/(6) + i sin" " (pi)/(6)) (cos" " (pi)/(12) + i sin" " (pi)/(12))

Find the rectangular form of the complex numbers. (cos" " (pi)/(6) - i sin" " (pi)/(6))/(2(cos" " (pi)/(3) + i sin" " (pi)/(3)))

Find the product 3/2 (cos (pi)/3 + i sin (pi)/3).6(cos (5pi)/6 + i sin (5pi)/6) in rectangular form.

FULL MARKS-COMPLEX NUMBERS -EXERCISE - 2.9
  1. Simplify (si n (pi)/6 + i co s (pi)/6)^(18).

    Text Solution

    |

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

    Text Solution

    |

  3. The value of sum(i=1)^(13) (n^(n) + i^(n-1)) is

    Text Solution

    |

  4. The area of the triangle formed by the complex numbers z, iz, and z + ...

    Text Solution

    |

  5. The conjugate of a complex number is (1)/(i-2). Then, the complex numb...

    Text Solution

    |

  6. If z= ((sqrt(3) + i)^(3) (3i+4)^(2))/((8 + 6i)^(2)), then |z| is equal...

    Text Solution

    |

  7. If z is non zero complex number, such that 2i z^(2) = bar(z),then |z| ...

    Text Solution

    |

  8. If |z-2 + i|le2, then the greatest value of |z| is

    Text Solution

    |

  9. If |z - (3)/(z)| = 2, then the least value of |z| is

    Text Solution

    |

  10. If |z| = 1, then the value of (1+z)/(1 +bar(z)).

    Text Solution

    |

  11. The solution of the equation |z| -z = 1 + 2i is

    Text Solution

    |

  12. If |z(1)| = 1, |z(2)| = 2, |z(3)| = 3 and |9z(1)z(2) + 4z(1) z(3) + z(...

    Text Solution

    |

  13. If z is a complex number such that z in CC\\RR, and z + (1)/(z) in RR,...

    Text Solution

    |

  14. z(1), z(3), and z(3) are complex numbers such that z(1) + z(2) + z(3)=...

    Text Solution

    |

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

    Text Solution

    |

  16. If z = x + iy is a complex number such that |z + 2| = |z - 2|, then th...

    Text Solution

    |

  17. The principal argument of (3)/(-1 + i) is

    Text Solution

    |

  18. The principal argument of (sin 40^(@) + i cos 40^(@))^(5) is

    Text Solution

    |

  19. If (1 + i)(1 + 2i)(1 + 3i)….(1 + ni) = x + iy, then 2.5.10…(1 + n^(2))...

    Text Solution

    |

  20. If omega ne 1 is a cubic root of unit and (1 + omega)^(7) = A + Bomega...

    Text Solution

    |

  21. The principal argument of the complex number ((1 + i sqrt(3))^(2))/(4i...

    Text Solution

    |