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w=-1/2+根号3/2i,则w4+w2+1=
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w=-1/2+根号3/2i,则w4+w2+1=
▼优质解答
答案和解析
w=-1/2+根号3/2i=cos(2π/3) +sin(2π/3)*i
则：w^4+w²+1
=cos(8π/3) +sin(8π/3)*i +cos(4π/3) +sin(4π/3)*i +1
=cos(2π/3) +sin(2π/3)*i -cos(π/3) -sin(π/3)*i +1
=-cos(π/3) +sin(π/3)*i -cos(π/3) -sin(π/3)*i +1
=-2cos(π/3)+1
=0
则：w^4+w²+1
=cos(8π/3) +sin(8π/3)*i +cos(4π/3) +sin(4π/3)*i +1
=cos(2π/3) +sin(2π/3)*i -cos(π/3) -sin(π/3)*i +1
=-cos(π/3) +sin(π/3)*i -cos(π/3) -sin(π/3)*i +1
=-2cos(π/3)+1
=0
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