Home
Class 12
MATHS
If omega be a complex cube root of unit...

If `omega` be a complex cube root of unity, then the number `(1-omega-omega^2)^3+(omega-1-omega^2)^3+(omega^2-omega-1)^3` is: a. Divisible by 3 but not by 8 b. Divisible by 8 but not by 3 c. Divisible by both 3 & 8 d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6)+(1-omega^(2)+omega)^(6)=

If omega is a complex cube root of unity then (1-omega+omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

(2+omega+omega^2)^3+(1+omega-omega^2)^8-(1-3omega+omega^2)^4=1

If omega is complex cube root of unity (1-omega+ omega^2) (1-omega^2+omega^4)(1-omega^4+omega^8)(1-omega^8+omega^16)

If omega is a cube root of unity, then omega^(3) = ……

If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega be an imaginary cube root of unity, show that (1+omega-omega^2)(1-omega+omega^2)=4

If omega is a cube root of unity, then find the value of the following: (1-omega)(1-omega^2)(1-omega^4)(1-omega^8)

If omega is a cube root of unity, then 1+ omega^(2)= …..

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Evaluate the following: lim(xrarr0)(sqrt(a+x)-sqrt(a-x))/x

    Text Solution

    |

  2. If cos^(-1)((n)/(2pi))lt(2pi)/(3) then maximum and minimum values of i...

    Text Solution

    |

  3. If omega be a complex cube root of unity, then the number (1-omega-om...

    Text Solution

    |

  4. The mean deviation about median of variates 13, 14, 15,...., 99, 100 i...

    Text Solution

    |

  5. Evaluate the following: (lim)(x -> -2)(3x^2+2x-8)/(x^3+8)

    Text Solution

    |

  6. If z and bar z represent adjacent vertices of a regular polygon of n s...

    Text Solution

    |

  7. The algebraic sum of deviations of 10 observations measured from 15 is...

    Text Solution

    |

  8. If the letters of the word ''REGULATIONS'' be arranged at random, fin...

    Text Solution

    |

  9. Let |z1|=|"z"2|="p"/2 then "|z1+z2|^2+|z1-z2|^2= a.p^2 b. (p^2)...

    Text Solution

    |

  10. Evaluate the following: lim(xrarr2)(x^2-4)/(sqrt(3x-2)-sqrt(6-x))

    Text Solution

    |

  11. Let f:[-(pi)/(3), (2pi)/(3)] to [0,4] be a function defined as f(x)=sq...

    Text Solution

    |

  12. If 3^(49)(x+i y)=(3/2+(sqrt(3))/2i)^(100) and x=k y then k is: a.-...

    Text Solution

    |

  13. Evaluate: ("lim")(xvec0)(s nx^0)/x

    Text Solution

    |

  14. If mean of squares of deviations of a set of n observations about -2a ...

    Text Solution

    |

  15. If complex number (3+2i s in x)/(1-2i s in x) is purely imaginary then...

    Text Solution

    |

  16. Evaluate the following: (lim)(xvecpi/2)(sin x)/x

    Text Solution

    |

  17. If ( x )1a n d( x )2 are the means of two distributions such that ( ...

    Text Solution

    |

  18. Let f, g and h be the lengths of the perpendiculars from the circumcen...

    Text Solution

    |

  19. The probability of a shooter hitting a target is 3/4 . How many minimu...

    Text Solution

    |

  20. If the standard deviation of a variable xi ssigma , then standard devi...

    Text Solution

    |