Home
Class 12
MATHS
If omega is an imaginary fifth root of u...

If `omega` is an imaginary fifth root of unity, then find the value of `loe_2|1+omega+omega^2+omega^3-1//omega|dot`

Text Solution

Verified by Experts

Here, `omega^(5)=1.` Therefore, `omega^(-1)=omega^(4)`
Also, `1+omega+omega^(2)+omega^(3)+omega^(4)=0`
`:." "log_(2)|1+omega+omega^(2)+omega^(3)-(1)/(omega)|`
`=log_(2)|1+omega+omega^(2)+omega^(3)-omega^(4)|`
`=log_(2)|-2omega^(4)|=log_(2)2=1" "(because|omega|=1)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

If omega is an imaginary fifth root of unity, then find the value of log_2|1+omega+omega^2+omega^3-1//omega|dot

If omega is an imaginary cube root of unity, then the value of (1+ omega- omega^(2))(1- omega + omega ^(2)) is-

If omega is an imaginary cube root of unity, then the value of the determinant |(1+omega,omega^(2),-omega),(1+omega^(2),omega,-omega^(2)),(omega+omega^(2),omega,-omega^(2))| is

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

If omega be the imaginary cube root of unity then the value of omega^(241) will be

If omega and omega^2 be the imaginary cube roots of unity then find the value of (3+3omega+5omega^2)^6-(2+6omega+2omega^2)^3

If omega is an imaginary cube root of untiy then the value of the determinant |{:(1+omega,omega^(2),-omega),(1+omega^(2),omega,-omega^(2)),(omega+omega^(2),omega,-omega^(2)):}|=

If omega is an imaginary cube root of unity. Find the value of the expression 1(2- omega)(2-omega^(2))+2(3-omega) +...+ (n-1)(n-omega)(n-omega^(2)) .

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

CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  1. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, the...

    Text Solution

    |

  2. If z=z0+A( z -( z )0), w h e r eA is a constant, then prove that loc...

    Text Solution

    |

  3. z1a n dz2 are the roots of 3z^2+3z+b=0. if O(0),(z1),(z2) form an equi...

    Text Solution

    |

  4. Let z(1),z(2) and z(3) be three complex number such that |z(1)-1|= |z...

    Text Solution

    |

  5. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

    Text Solution

    |

  6. In the Argands plane what is the locus of z(!=1) such that a rg{3/2((2...

    Text Solution

    |

  7. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

    Text Solution

    |

  8. If z1, z2, z3 are complex numbers such that (2//z1)=(1//z2)+(1//z3), t...

    Text Solution

    |

  9. A(z1),B(z2),C(z3) are the vertices of he triangle A B C (in anticlockw...

    Text Solution

    |

  10. If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-...

    Text Solution

    |

  11. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

    Text Solution

    |

  12. Complex numbers z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

    Text Solution

    |

  13. Let z1, z2a n dz3 represent the vertices A ,B ,a n dC of the triangle ...

    Text Solution

    |

  14. F a=cos(2pi//7)+isin(2pi//7) , then find the quadratic equation whose ...

    Text Solution

    |

  15. If omega is an imaginary fifth root of unity, then find the value of l...

    Text Solution

    |

  16. If 1, alpha(1), alpha(2), alpha(3),…….,alpha(s) are ninth roots of uni...

    Text Solution

    |

  17. find the sum of squares of all roots of the equation. x^(8) - x^(7) ...

    Text Solution

    |

  18. Find roots of the equation (z + 1)^(5) = (z - 1)^(5).

    Text Solution

    |

  19. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

    Text Solution

    |

  20. Let 1, z(1),z(2),z(3),…., z(n-1) be the nth roots of unity. Then pro...

    Text Solution

    |