If ω is a complex cube root of unity then ∣∣
∣
∣∣11+ω1+ω21+ω1+ω211+ω211+ω∣∣
∣
∣∣=
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Q2
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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Q3
If (a+ω)−1+(a+ω)−1+(c+ω)−1+(d+ω)−1=2ω−1 and (a+ω′)−1+(b+ω′)−1+(c+ω′)−1+(d+ω′)−1=2(ω′)−1, where ω and ω′ are the imaginary cube roots of unity, then the value of (a+1)−1+(b+1)−1+(c+1)−1+(d+1)−1 is
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Q4
If one of the cube roots of 1 be ω, then ∣∣
∣
∣∣11+ω2ω21−i−1ω2−1−i−1+ω−1∣∣
∣
∣∣
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Q5
If ω is complex (non real) cube root of 1 then show that ∣∣
∣
∣∣1ωω2ωω21ω21ω∣∣
∣
∣∣=0.