Q.

If w is a complex cube root of unity then the value of cos1-w1-w2+2-w2-w2++10-w10-w2π9 is

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a

-12

b

1

c

–1 

d

12

answer is B.

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Detailed Solution

  cos(1-w) 1-w2+(2-w) 2-w2...+(10-w) 10-w2 π9  cos r=110 r2-r(w+w2)+w3 π9  cos r=110 r2+r+1 π9  cos10 (11) (21)6+10 (11)2+10 π9  cos385+55+10 π9  cos450π9  cos50π =1

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