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If (a+ω)−1+(b+ω)−1+(c+ω)−1+(d+ω)−1=2ω−1,(a+ω)−1+(b+ω)−1+(c+ω)−1+(d+ω)−1=2(ω′)−1 where ω and ω′ are the imaginary cube root of unity, prove that (a+ω)−1+(b+ω)−1+(c+ω)−1+(d+ω)−1=2. |
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Answer» If (a+ω)−1+(b+ω)−1+(c+ω)−1+(d+ω)−1=2ω−1,(a+ω)−1+(b+ω)−1+(c+ω)−1+(d+ω)−1=2(ω′)−1 where ω and ω′ are the imaginary cube root of unity, prove that (a+ω)−1+(b+ω)−1+(c+ω)−1+(d+ω)−1=2. |
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