求x^10=1的所有解

问题描述:

求x^10=1的所有解

1=cos0+isin0,r=1,θ=010√(cos0+isin0)=cos(2kπ/n)+isin(2kπ/n),n=10,k=0,1,2,3,4,5,6,7,8,9所以x^10=1的10个解为1,cos(π/5)+isin(π/5),cos(2π/5)+isin(2π/5),cos(3π/5)+isin(3π/5),cos(4π/5)+isin(4π/5)...