8的1/3次方是多少？复数域中

(x+yi)^3=8(x,y属于R
(x^2-y^2+2xyi)(x+yi)=8
(x^3-y^3i+3x^2*yi-3xy^2)=8
x^3-3xy^2=8
3x^2*y-y^3=0
x=2,y=0
x=-1,y=根号3
x=-1,y=-根号3
z=-1+根号3
z=-1-根号3
z=2

x^3=8,x^3-2^3=0,(x-2)(x^2+2x+4)=0
(1).x-2=0,x1=2
(2).x^2+2x+4=0,x=[-2±(√12)i]/2=-1±√3i
∴x1=2,x2=-1+√3i,x3=-1-√3i

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