虚数化简1/4*(-4+4*i*3^(1/2))^(1/3)+1/(-4+4*i*3^(1/2))^(1/3)-1/8*(-4+4*i*3^(1/2))^(1/3)-1/2/(-4+4*i*3^(1/2))^(1/3)+1/4*i*3^(1/2)*(1/2*(-4+4*i*3^(1/2))^(1/3)-2/(-4+4*i*3^(1/2))^(1/3))-1/8*(-4+4*i*3^(1/2))^(1/3)-1/2/(-4+4*i*3^(1/2))^(1/3)-1/4*i*3^

Question

虚数化简
1/4*(-4+4*i*3^(1/2))^(1/3)+1/(-4+4*i*3^(1/2))^(1/3) -1/8*(-4+4*i*3^(1/2))^(1/3)-1/2/(-4+4*i*3^(1/2))^(1/3)+1/4*i*3^(1/2)*(1/2*(-4+4*i*3^(1/2))^(1/3)-2/(-4+4*i*3^(1/2))^(1/3)) -1/8*(-4+4*i*3^(1/2))^(1/3)-1/2/(-4+4*i*3^(1/2))^(1/3)-1/4*i*3^(1/2)*(1/2*(-4+4*i*3^(1/2))^(1/3)-2/(-4+4*i*3^(1/2))^(1/3)) 不要三角形式,也不要极坐标,不要小数,用复根式和分式表示即可
题有些看不清
第一个1/4*(-4+4*i*3^(1/2))^(1/3)+1/(-4+4*i*3^(1/2))^(1/3)
第二个-1/8*(-4+4*i*3^(1/2))^(1/3)-1/2/(-4+4*i*3^(1/2))^(1/3)+1/4*i*3^(1/2)*(1/2*(-4+4*i*3^(1/2))^(1/3)-2/(-4+4*i*3^(1/2))^(1/3))
第三个-1/8*(-4+4*i*3^(1/2))^(1/3)-1/2/(-4+4*i*3^(1/2))^(1/3)-1/4*i*3^(1/2)*(1/2*(-4+4*i*3^(1/2))^(1/3)-2/(-4+4*i*3^(1/2))^(1/3))
作出正确答案者,直接追加100财富

Answer 1

x^3-1=(x-1)(x^2+x+1)
x^2+x+1的一个根为（-1-根号3*i)/2
所以（-1-根号3*i)/2也是x^3-1的根
所以{（-1-根号3*i)/2}^3=1
所以（-1-根号3*i)^3=8
所以（1+根号3*i)^3=-8
所以6次方=64
满意请采纳.