4. If (ω ≠ 1) be a cube root of unity and (1 + ω)⁷ = l + mω, then

(A) l = 0, m = 1

(B) l = 1, m = 1

(C) l = 1, m = 0

(D) l = –1, m = 1

please solve it

Dear student,

1+w=-w^2

Therefore LHS=-w^14=-w^2=1+w=l+mw

Therefore

l=1

m=1

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All the best.

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

1+w+w² =0          &    w³=1

(1+w)⁷ =  l + mw

  (-w²)⁷ = l + mw

  (-1)⁷ (w¹⁴) = l + mw

   (-1)(w³)⁴ w² = l + mw

    -w² = l + mw

   1 + w = l + mw

    l=1 ,m=1

hence B is correct

thankx