求出复数(-8i)开三次方的所有单根

Question

求出复数(-8i)开三次方的所有单根

Answer 1

(z)^1/n=|z|^1/n *{ [cos（a+2kπ)/n] + i [sin（a+2kπ)/n]} (其中a是z的辐角主值.k=0,1,n-1)
(-8i)^1/3=8^1/3 *{ [cos（-π/2+2kπ)/3] + i [sin（-π/2+2kπ)/3]} k=0,1,2
k=0,时 (-8i)^1/3=√3-i
k=1,时 (-8i)^1/3=2i
k=2,时 (-8i)^1/3=-√3+i