Home
Class 12
MATHS
If omegane1 is a cube root of unity, sho...

If `omegane1` is a cube root of unity, show that the roots of the equation `(z-1)^(3)+8=0` are `-1,1-2omega,1-2omega^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
From (1),(2) and (3), the roots are -1, 1 -`2 omega^(2)` and 1 - `2omega^(2)`.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    SURA PUBLICATION|Exercise EXERCISE 2.9|25 Videos

  • COMPLEX NUMBERS

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS (1 MARK)|20 Videos

  • COMPLEX NUMBERS

    SURA PUBLICATION|Exercise EXERCISE 2.7|12 Videos

  • APPLICATIONS OF VECTORA ALGEBRA

    SURA PUBLICATION|Exercise ADDITIONAL QUESTIONS ( 5 MARKS )|5 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    SURA PUBLICATION|Exercise 5 MARKS|4 Videos

Similar Questions

Explore conceptually related problems

If the cube roots of unity are 1, omega, omega^(2) then the roots of the equation (x-1)^(3)+8=0 , are

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

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 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

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 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

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