复数的三角形式及运算 (-1+√3i)^6-(-1-√3i)^6怎么算

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复数的三角形式及运算 (-1+√3i)^6-(-1-√3i)^6怎么算
复数的三角形式及运算 (-1+√3i)^6-(-1-√3i)^6怎么算

复数的三角形式及运算 (-1+√3i)^6-(-1-√3i)^6怎么算
复数的三角形式及运算 (-1+√3i)⁶-(-1-√3i)⁶怎么算
原式={2[cos(2π/3)+isin(2π/3)]}⁶-{2[cos(4π/3)+isin(4π/3)]}⁶
=2⁶[cos(4π)+isin(4π)-cos(4π)-isin(4π)]=0

(-1+√3i)^2=1-2√3i+3i^2=1-2√3i-3=-2-2√3i=-2(1+√3i)
所以(-1+√3i)^3=-2(1+√3i)(-1+√3i)=-2(3i^2-1)=8
所以(-1+√3i)^6=(8)^2=64
同理(-1-√3i)^6=64
所以(-1+√3i)^6-(-1-√3i)^6=0