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
设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值
设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值
z=-1/2-(根号3)/2 i
z^2=1/4-3/4+(根号3)/2 i=-1/2+(根号3)/2 i
z^3=1/4+3/4=1
z^2+z+1==-1/2-(根号3)/2 i - 1/2+(根号3)/2 i + 1=0
根据欧拉公式:e^(ix) = cos(x) + i*sin(x)
所以Z = e^[i(-2π/3)]
因此Z^2 = e^[i(-4π/3)] = -1/2 + i*[(根号3)/2]
同时Z^3 = e^[i(-2π)] = 1
而Z^2 + Z + 1 = 0
设Z=cos2π/3-isin2π/3,求Z^2,Z^3及Z^2+Z+1的值
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