复数,等比数列求和
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z=cos(4π/5)+isin(4π/5)
z^4=cos(16π/5)+isin(16π/5)=-cos(π/5)-isin(π/5)
z^8=cos(32π/5)+isin(32π/5)=cos(2π/5)+isin(2π/5)
z^12=cos(48π/5)+isin(48π/5)=cos(2π/5)-isin(2π/5)
z^16=cos(64π/5)+isin(64π/5)=-cos(π/5)+isin(π/5)
1+z^4+z^8+z^12+z^16
=1-cos(π/5)-isin(π/5)+cos(2π/5)+isin(2π/5)+cos(2π/5)-isin(2π/5)-cos(π/5)+isin(π/5)
=1-2cos(π/5)+2cos(2π/5)
z^4=cos(16π/5)+isin(16π/5)=-cos(π/5)-isin(π/5)
z^8=cos(32π/5)+isin(32π/5)=cos(2π/5)+isin(2π/5)
z^12=cos(48π/5)+isin(48π/5)=cos(2π/5)-isin(2π/5)
z^16=cos(64π/5)+isin(64π/5)=-cos(π/5)+isin(π/5)
1+z^4+z^8+z^12+z^16
=1-cos(π/5)-isin(π/5)+cos(2π/5)+isin(2π/5)+cos(2π/5)-isin(2π/5)-cos(π/5)+isin(π/5)
=1-2cos(π/5)+2cos(2π/5)
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