Home
Class 12
MATHS
Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=...

Assertion (A) : `(sqrt3+i)^6+(sqrt3-i)^6=-128`
Reason (R) : If n is a positive integer then
`(sqrt3+i)^n+(sqrt3-i)^n=2^(n+1)cos(npi)/(6)`

A

`2^(n+1)cos(npi)/(2)`

B

`2^(n+1)cos(npi)/(3)`

C

`2^(n+1)cos(npi)/(5)`

D

`2^(n+1)cos(npi)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise EXERCISE -II|58 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise (Level-2)|38 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH SERIES|Exercise Practice Exercise|62 Videos

Similar Questions

Explore conceptually related problems

If n is a positive niteger, then (sqrt3+i)^(n)+(sqrt3-i)^(n)

(sqrt3+i)^7+(sqrt3-i)^7=

If n is a positive integer, then (1+i)^n+(1-i)^n=

If n is a positive integer prove that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos((n pi)/(2))

(sqrt3+i)^(7)+(sqrt3-i)^(7)

If n is a positive integer, show that (1 + i)^(n) + (1 - i)^(n) = 2 ^((n+2)/2) cos ((npi)/4) .

A : (1+i)^(6)+(1-i)^(6)=0 R : If n is a positive integer then (1+i)^(n)+(1-i)^(n)=2^((n//2)+1).cos""(npi)/(4)

When n=8,(sqrt(3)+i)^(n)+(sqrt(3)-i)^(n)=

If n is integer then show that (1 + i)^(2n) + (1 - i)^(2n) = 2 ^(n+1) cos . (npi)/2 .

AAKASH SERIES-DEMOIVRE'S THEOREM-PRACTICE EXERCISE
  1. If ((sqrt3//2+(1//2)i)/(sqrt3//2-(1//2)i))^(120)=p+iq,then

    Text Solution

    |

  2. If n is a positive integer, then (1+i)^n+(1-i)^n=

    Text Solution

    |

  3. Assertion (A) : (sqrt3+i)^6+(sqrt3-i)^6=-128 Reason (R) : If n is ...

    Text Solution

    |

  4. (sqrt3+i)^7+(sqrt3-i)^7=

    Text Solution

    |

  5. (cos""(pi)/(6)+isin""(pi)/(6))^(1//2)+(cos""(pi)/(6)-isin""(pi)/(6))^(...

    Text Solution

    |

  6. One value of (1+isqrt3)^(3//4)+(1-isqrt3)^(3//4) is equal to

    Text Solution

    |

  7. One of the value of [cos(pi//6)-isin(pi//6)]^(11//2)/[cos(pi//6)+isin(...

    Text Solution

    |

  8. If x=cosalpha+isinalpha,y=cosbeta+isinbeta," then "(x)/(y)+(y)/(x)

    Text Solution

    |

  9. If x=cisalpha,y=cisbeta" then " x^3y^4-(1)/(x^3y^4)=

    Text Solution

    |

  10. If a,b and c are in G.P then (b - a)/(b - c) + (b + a)/(b + c)

    Text Solution

    |

  11. cis(pi)/(10).cis(2pi)/(10).cis(3pi)/(10).cis(4pi)/(10)=

    Text Solution

    |

  12. If xn=cos(pi/2^n)+isin(pi/2^n), then x1 x2 x3......infinity

    Text Solution

    |

  13. If x(n)=cos((pi)/(4^(n)))+i sin ((pi)/(4^(n))), then x(1), x(2), x(3)....

    Text Solution

    |

  14. The continued product of the four values of (1-isqrt3)^(3//4) is

    Text Solution

    |

  15. The continued product of all values of root(5)(4) is

    Text Solution

    |

  16. sum(r=1)^(8)[sin(2pir//9)+icos(2pir//9)]=

    Text Solution

    |

  17. The values of sum(m=1)^(10)[sin(2pim//11)-icos(2pim//11)] is

    Text Solution

    |

  18. If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma then sin3alph...

    Text Solution

    |

  19. If cos alpha+cos beta+cos gamma=0 & sin alpha +sin beta +sin gamma=0. ...

    Text Solution

    |

  20. If cos alpha+cosbeta+cosgamma = 0 = sinalpha + sinbeta + singamma then...

    Text Solution

    |