Home
Class 11
MATHS
If omega is an imaginary cube root of un...

If `omega` is an imaginary cube root of unity, then `(1+omega-omega^2)^7` is equal to

A

`128omega`

B

`-128omega`

C

`128omega^2`

D

`-128omega^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If omega is an imaginary cube root of unity, then show that (1-omega)(1-omega^2)(1-omega^4) (1-omega^5)=9

If omega is an imaginary cube root of unity, then show that (1-omega+omega^2)^5+(1+omega-omega^2)^5 =32

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 1+omega = …..

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

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

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If omega be an imaginary cube root of unity, show that 1+omega^n+omega^(2n)=0 , for n=2,4

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

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a ,b ,c and u ,v ,w are the complex numbers representing the vertic...

    Text Solution

    |

  2. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)++a(n...

    Text Solution

    |

  3. If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 ...

    Text Solution

    |

  4. If z=x+iy is a complex number with x, y in Q and |z| = 1, then show ...

    Text Solution

    |

  5. Referred to the principal axes as the axes of co ordinates find the eq...

    Text Solution

    |

  6. Find the area bounded by |arg z|lt=pi//4 and |z-1|<|z-3|dot

    Text Solution

    |

  7. sum(k=1)^6 (sin,(2pik)/7 -icos, (2pik)/7)=?

    Text Solution

    |

  8. If the equation a x^2+b x+c=0(a &gt;0) has two real roots alphaa n db...

    Text Solution

    |

  9. If fig shows the graph of f(x)=a x^2+b x+c ,t h e n Fig a. c<0 b. b c...

    Text Solution

    |

  10. If det|6i -3i 1 4 3i-1 20 3 i|=x+i y , then a.x=3,y=1 b. x=1...

    Text Solution

    |

  11. Let z=x+i y be a complex number, where xa n dy are real numbers. Let...

    Text Solution

    |

  12. If z=((sqrt(3))/2+i/2)^5+((sqrt(3))/2-i/2)^5 , then prove that I m(z)=...

    Text Solution

    |

  13. The value of sum(n=1)^(13) (i^n+i^(n+1)), where i =sqrt(-1) equals (...

    Text Solution

    |

  14. If c!=0 and the equation p//(2x)=a//(x+c)+b//(x-c) has two equal roo...

    Text Solution

    |

  15. If the equation 4x^2-x-1=0 and 3x^2+(lambda+mu)x+lambda-mu=0 have a r...

    Text Solution

    |

  16. Express the following in a+i b form: ((cos2theta-isin2theta)^4(cos4...

    Text Solution

    |

  17. The roots of the equation t^3+3a t^2+3b t+c=0a r ez1, z2, z3 which rep...

    Text Solution

    |

  18. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

    Text Solution

    |

  19. If 'z, lies on the circle |z-2i|=2sqrt2, then the value of arg((z...

    Text Solution

    |

  20. If the equation whose roots are the squares of the roots of the cubic ...

    Text Solution

    |