Complex Numbers 5 Question 14

15.

The value of the expression

1(2ω)(2ω2)+2(3ω)(3ω2)+

+(n1)(nω)(nω2),

where, ω is an imaginary cube root of unity, is….

(1996, 2M)

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Answer:

Correct Answer: 15. n(n+1)22n

Solution:

  1. Here, Tr=(r1)(rω)(rω)2]=(r31)

Sn=r=1n(r31)=n(n+1)22n



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