Home
Class 12
MATHS
If omega pm 1 is a cube root of unity, s...

If `omega pm` 1 is a cube root of unity, show that `(a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = -1`

Text Solution

Verified by Experts

The correct Answer is:
`-1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.9|25 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.7|6 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    FULL MARKS|Exercise Additional Questions Solved|29 Videos

Similar Questions

Explore conceptually related problems

If omega pm 1 is a cube root of unity, show that (1 - omega + omega^(2))^(6) + (1 + omega - omega^(2))^(6) = 128

If omega pm 1 is a cube root of unity, show that (1 + omega) (1 + omega^(2))(1 + omega^(4))(1 + omega^(8))…(1 + omega^(2^(11))) = 1

Knowledge Check

  • If omega is a cube root of unity, then the value of (1 - omega + omega^2)^4 + (1 + omega - omega^2)^(4) is ……….

    A
    `-16`
    B
    `0`
    C
    `-32`
    D
    `32`

  • If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=

    A
    `1`
    B
    `omega`
    C
    `omega^(2)`
    D
    `0`

  • If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

    A
    `a^(3)+b^(3)`
    B
    `a^(3)-b^(3)`
    C
    `a^(2)+b^(2)`
    D
    `a^(2)-b^(2)`

    • Similar Questions

    Explore conceptually related problems

    If omega ne 1 is a cube root of unity, then show that (a+bomega+comega^(2))/(b+comega+aomega^(2))+(a+bomega+comega^(2))/(c+aomega+bomega^(2))=1

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

    If 1, omega omega^(2) are the cube roots of unity then show that (1 + 5omega^(2) + omega^(4)) ( 1 + 5omega + omega^(2)) ( 5 + omega + omega^(5)) = 64.

    If omega ne 1 is a cube root of unity, show that (i) (1-omega+omega^(2))^(6)+(1+omega-omega^(2))^(6)=128 (ii) (1+omega)(1+omega^(2))(1+omega^(4))(1+omega^(8))…2n terms=1

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

    Home
    Profile