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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

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

Grade:12

3 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

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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Sagar Singh

B.Tech, IIT Delhi



vikas askiitian expert
509 Points
13 years ago

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

 

pranay -askiitians expert
44 Points
13 years ago

thankx

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