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设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值,
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设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值,
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答案和解析
少了个i
Z=cos2π/3-isin2π/3
所以Z^2=cos(2×2π/3)-isin(2×2π/3)
=cos4π/3-isin4π/3
=-(1+i√3)/2
Z^3=cos(3×2π/3)-isin(3×2π/3)
=cos2π-isin2π
=1
Z^2+Z+1
=-(1+i√3)/2+(-1-i√3)/2+1
=-i√3
Z=cos2π/3-isin2π/3
所以Z^2=cos(2×2π/3)-isin(2×2π/3)
=cos4π/3-isin4π/3
=-(1+i√3)/2
Z^3=cos(3×2π/3)-isin(3×2π/3)
=cos2π-isin2π
=1
Z^2+Z+1
=-(1+i√3)/2+(-1-i√3)/2+1
=-i√3
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