The value of the expression 2(1+1ω)(1+1ω2)+3(2+1ω)(2+1ω2)+4(3+1ω) – InterviewSolution

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1.	The value of the expression 2(1+1ω)(1+1ω2)+3(2+1ω)(2+1ω2)+4(3+1ω)(3+1ω2)+⋯+(n+1)(n+1ω)(n+1ω2), where ω is an imaginary cube root of unity, is
Answer» The value of the expression $2 (1 + \frac{1}{ω}) (1 + \frac{1}{ω^{2}}) + 3 (2 + \frac{1}{ω}) (2 + \frac{1}{ω^{2}}) + 4 (3 + \frac{1}{ω}) (3 + \frac{1}{ω^{2}}) + \dots + (n + 1) (n + \frac{1}{ω}) (n + \frac{1}{ω^{2}}),$ where $ω$ is an imaginary cube root of unity, is

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