高中复数题.(-1+√3i)的五次幂/(1+√31)的值?
问题描述：
高中复数题.(-1+√3i)的五次幂/(1+√31)的值?
最后得-16.怎么算的.
答
-1+√3i=2(cos(2/3π)+isin(2/3π))1+√3i=2(cos(π/3)+isin(π/3))所以原式=2^5(cos(10/3π)+isin(10/3π))/[2(cos(π/3)+isin(π/3))]=2^4(cos(4/3π)+isin(4/3π))/(cos(π/3)+isin(π/3))=2^4(cosπ+isinπ)=-16...