Home
Class 12
MATHS
If 1,omega,omega^2 are the cube roots of...

If `1,omega,omega^2` are the cube roots of unity, then `/_\`

is equal to.....

Text Solution

Verified by Experts

`Delta=1(omega^(3n)-1)+omega^(n)(omega^(2n)-omega^(2n))+omega^(2n)(omega^(n)-omega^(4n))`
`Delta=[(omega^(3))^(n)-1]+0+omega^(2n)[omega^(n)-(omega^(3))^(n)*omega^(n)]`
`Delta=1-1+0+omega^(2n)[omega^(n)-omega^(n)]=0`.
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 28

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION-2)|5 Videos
  • JEE MAIN REVISION TEST - 4 JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

If 1, omega, omega^(2) are three cube roots of unity, prove that (1 + omega - omega^(2)) (1- omega + omega^(2))=4

If 1, omega, omega^(2) are three cube roots of unity, prove that (1)/(1 + omega) + (1)/(1+ omega^(2))=1

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

If 1, omega, omega^(2) are the three cube roots of unity, then simplify: (3 + 5omega + 3omega^(2))^(2) (1 + 2omega + omega^(2))

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega) (1- omega^(2))= 3

If 1, omega, omega^(2) are three cube roots of unity, prove that (1- omega- omega^(2))^(6)= 64

If 1, omega, omega^(2) are three cube roots of unity, prove that (1+ omega- omega^(2))^(3)= (1- omega + omega^(2))^(3)= -8

If 1 , omega, omega^(2) are cube roots of unity then the value of (3 + 5omega+3omega^(2))^(3) is

If 1, omega, omega^(2) are the cube roots of unity, prove that omega^(n) + omega^(2n) =2 or -1 according as n is a multiple of 3 or any other integer.

If 1, omega, omega^(2) are three cube roots of unity, prove that (3+ 5omega + 3omega^(2))^(6) = (3 + 5omega^(2) + 3omega)^(6)= 64

VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 29 (2020)-MATHEMATICS
  1. Matrix A such that A^(2)=2A-I, where I is the identity matrix, then fo...

    Text Solution

    |

  2. If Real ((2z-1)/(z+1))=1, then locus of z is , where z=x+iy and i=sqrt...

    Text Solution

    |

  3. Let A(3, 2) and B(6, 5) be two points and a point C (x,y) is chosen on...

    Text Solution

    |

  4. The equation of the circle, which touches the parabola y^2=4x at (1,2)...

    Text Solution

    |

  5. There are exactly two points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 ...

    Text Solution

    |

  6. int(a^4)^(b^4)(f(sqrtx))/((sqrtx)[f(a^2+b^2-sqrtx)+f(sqrtx)])dx is equ...

    Text Solution

    |

  7. The area bounded by the curves x + y = 2 and y = x^2 above x-axis in ...

    Text Solution

    |

  8. Solution of (sin x)(dy)/(dx) = y ln y , given y ((pi)/2) = e

    Text Solution

    |

  9. If y^x=x^y then (dy)/(dx) at x=1, y=1 is

    Text Solution

    |

  10. f(x)=(x^2-1)|x^2-3x+2|+cos|x| is not differentiable at x=a, then sum(r...

    Text Solution

    |

  11. If veca = hati + hatj + hatk & vecb = hati - hatj + hatk are the side...

    Text Solution

    |

  12. lim(x->e) (lnx-1)/(x-e)

    Text Solution

    |

  13. if the system of linear equations {:(x+2ay+az=0),(x+3by+bz=0),(x+4c...

    Text Solution

    |

  14. Variance of 1st 10 natural nos. is m & mean of first 10 odd natural nu...

    Text Solution

    |

  15. Find the expected value of the experiment “tossing 3 coins simultaneou...

    Text Solution

    |

  16. The greatest +ve integer k, for which 4^k+1 is factor of sum 1+2+2^2+....

    Text Solution

    |

  17. If tan prop &tan beta are the roots of the equation bx^2+ax-1=0,bcance...

    Text Solution

    |

  18. If 1,omega,omega^2 are the cube roots of unity, then /\ is equal...

    Text Solution

    |

  19. If four numbers. in decreasing A.P, a, b, c, d have their sum as 20 & ...

    Text Solution

    |

  20. If g(x)=x^3+x-2 and g(f(x))=x^3+3x^2+4x then f(1)+f(2) is equal to

    Text Solution

    |