Home
Class 12
MATHS
If z + (1)/(z) = 2 cos theta, z in "C th...

If `z + (1)/(z) = 2 cos theta, z in "C then z"^(2n) - 2z^(n) cos (n theta)` is equal to

A

1

B

0

C

-1

D

`-n`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 2|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE LEVEL 3|1 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise EXERCISE|20 Videos

  • CIRCLES AND SYSTEMS OF CIRCLES

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|17 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

Similar Questions

Explore conceptually related problems

If z=-2 + 2 sqrt3i then z^(2n) + z^(n) + 2^(4n) may be equal to

If z+1/z=2cos theta, prove that |(z^(2n)-1)/(z^(2n)+1)|=|tan n theta|

If z=-2+2sqrt(3)i, then z^(2n)+2^(2n)*z^(n)+2^(4n) is equal to

If tan 3 theta + tan theta =2 tan 2 theta , then theta is equal to (n in Z)

If z_(1) and z_(2) are two nonzero complex numbers and theta is a real number, then (1)/(|z_(1)|^(2) + |z_(2)|^(2))[|(cos theta)z_(1) - (sin theta)z_(2)|^(2) + |(sin theta)z_(1) + (cos theta) z_(2)|^(2) ] is equal to ________

"cot" theta = "sin" 2 theta, theta ne n pi, n in Z, "if" theta equals

If z=cos theta+i sin theta, then the value of (z^(2n)-1)/(z^(2n)+1)(A)i tan n theta(B)tan n theta(C)i cot n theta(D)-i tan n theta

MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE LEVEL 1
  1. If |z1|=|z2|=|z3|=1 then value of |z1-z3|^2+|z3-z1|^2+|z1-z2|^2 cannot...

    Text Solution

    |

  2. Let z1z2,z3, be three complex number such that z1+z2+z3=0 and |...

    Text Solution

    |

  3. Let z(1), z(2), z(3) be three complex numbers such that |z(1)| = |z(2)...

    Text Solution

    |

  4. Suppose z is a complex number such that z ne -1, |z| = 1, and arg(z) =...

    Text Solution

    |

  5. Let a = Im((1+z^(2))/(2iz)), where z is any non-zero complex number. T...

    Text Solution

    |

  6. Number of complex numbers such that |z| = 1 and z = 1 - 2 bar(z) is

    Text Solution

    |

  7. Let z(1), z(2) be two complex numbers such that z(1) ne 0 and z(2)//z(...

    Text Solution

    |

  8. If z = i(1+sqrt(3)),"then"z^(4)+2z^(3)+4z^(2) + 5 is equal to

    Text Solution

    |

  9. If the fourth roots of unity are z1, z2, z3, z4 and z1^2+z2^2+z3^2+z4^...

    Text Solution

    |

  10. Suppose arg (z) = - 5 pi//13, then arg((z + bar(z))/(1+z bar(z))) is

    Text Solution

    |

  11. The number of values of theta in (0, pi], such that (cos theta + i sin...

    Text Solution

    |

  12. If z in C - {0, -2} is such that log((1//7)) |z-2| gt log((1//7)) |z| ...

    Text Solution

    |

  13. Im ((2z+1)/(iz+1))=5 represents

    Text Solution

    |

  14. If z1,z2 are two complex numbers such that Im(z1+z2)=0,Im(z1z2)=0, the...

    Text Solution

    |

  15. The number (1+ i)^n / (1 - i )^(n-2) is equal to

    Text Solution

    |

  16. Let omega ne 1, be a cube root of unity, and f : I rarr C be defined b...

    Text Solution

    |

  17. If z + (1)/(z) = 2 cos theta, z in "C then z"^(2n) - 2z^(n) cos (n the...

    Text Solution

    |

  18. If omega ne 1 is a cube root of unity, then z=sum(k=1)^(60)omega^(k) -...

    Text Solution

    |

  19. Let g(x) and h(x) be two polynomials with real coefficients. If p(x) =...

    Text Solution

    |

  20. If x^(2) - x + 1 divides the polynomial x^(n+1) - x^(n) + 1, then n mu...

    Text Solution

    |