在复数集C中分解因式x^6-1

x^6-1
=(x^3+1)(x^3-1)
=(x+1)(x^2-x+1)(x-1)(x^2+x+1)
=(x+1)(x-1)(x-1/2+i√3/2)(x-1/2-i√3/2)(x+1/2+i√3/2)(x+1/2-i√3/2)

x^6-1
=(x^3)^2-1
=(x^3+1)(x^3-1)
=(x+1)(x^2+1-x)(x-1)(x^2+1+x)
令x^2+1-x=0
用配方
(x-1/2)^2=-3/4
x=1/2+根号3/2*i
或1/2-根号3/2*i
同理x^2+1+x=0两根是
x=-1/2+根号3/2*i
或-1/2-根号3/2*i
(x+1)(x^2+1-x)(x-1)(x^2+1+x)
=(x+1)(x-1/2-根号3/2*i)(x-1/2+根号3/2*i)(x-1)(x+1/2+根号3/2*i)(x+1/2-根号3/2*i)

x^6-1=(x^3-1)(x^3+1)=(x-1)(x^2+x+1)(x+1)(x^2+x+1)
=(x-1)(x+1)[x-(-1+(3^1/2i)/2][x+(-1+(3^1/2i)/2][x-(1+(3^1/2i)/2][x+(1+(3^1/2i)/2]