✨ คำตอบที่ดีที่สุด ✨
ω⁵=1
所以1/(1+ω)+1/(1+ω²)+1/(1+ω³)+1/(1+ω⁴)
=[ 1/(1+ω)+1/(1+ω⁴)]+[1/(1+ω²)+1/(1+ω³)]
=[ 1/(1+ω)+1/(1+(1/ω))]+1/(1+ω²) +1/(1+(1/ω²))
= [1/(1+ω)+ω/(1+ω)]+[1/(1+ω²)+ω²/(1+ω²)]
=1+1=2
設ω=cos(2π/5)+isin(2π/5)
求1/(1+ω)+1/(1+ω²)+1/(1+ω³)+1/(1+ω⁴)=?
✨ คำตอบที่ดีที่สุด ✨
ω⁵=1
所以1/(1+ω)+1/(1+ω²)+1/(1+ω³)+1/(1+ω⁴)
=[ 1/(1+ω)+1/(1+ω⁴)]+[1/(1+ω²)+1/(1+ω³)]
=[ 1/(1+ω)+1/(1+(1/ω))]+1/(1+ω²) +1/(1+(1/ω²))
= [1/(1+ω)+ω/(1+ω)]+[1/(1+ω²)+ω²/(1+ω²)]
=1+1=2
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