Pure Maths MC

1.複數根沒辦法定順序
2.有一根為0
3.兩根相除之總和會有很多答案(不同順序),甚至不存在
例: x^3+x^2+x=0 => x=0, w, w^2 ,w=cos(2pi/3)+i sin(2pi/3)
0/w+ w/w^2= 1/w
0/w^2+ w^2/w= w兩者就不一樣了

Obviously x = 0 is a root of the equation.
The series is not well-defined for if we take alpha_i = 0, where 2 <= i <= n.

Any constraints to the order of the roots?

2009-02-16 00:54:11 補充：
Actually the order is important.
Consider the case when n = 4.
The equation is x^4 + x^3 + x^2 + x = 0, whose roots are 0, -1, +/-i.

Suppose α1=0, α2=-1, α3=i, α4=-i.
Required sum = 0 + i - 1 = i - 1.

Suppose α1=0, α2=i, α3=-1, α4=-i.
Required sum = 0 - i - i = -2i.
The sum depends on the order.