w=-1/2+根号3/2i,则w4+w2+1=

Question

w=-1/2+根号3/2i,则w4+w2+1=

Answer 1

2w+1=√3i
平方
4w²+4w+1=-3
所以w²+w+1=0
(w-1)(w²+ww+1)=0
w³-1=0
w³=1
所以原式=w*w³+w³/w+1
=w+1/w+1
=(w²+w+1)/w
=0