Question

在复数范围内分解因式：x^4+x^2y^2+y^4

Answer 1

=x^4+2x^2y^2+y^4-x^2y^2

=(x^2+y^2)^2-x^2y^2

=(x^2+xy+y^2)(x^2-xy+y^2)

=[(x+y/2)^2+3y^2/4][(x-y/2)^2+3y^2/4]

=(x+y/2+i√3y/2)(x+y/2-i√3y/2)(x-y/2+i√3y/2)(x-y/2-i√3y/2)