複數的極式與幾何意義

1.求方程式的根0=x^4+x^2+1=(y-1)(y^2+y+1).....y=x^2=y^3-1y^3=1=cos360°+jsin360°y=(cos360°+jsin360°)^(1/3)y1=cos120°+jsin120°.....戴美弗定理y2=cos240°+jsin240°y3=cos360°+jsin360°x1=+-(cos120°+jsin120°)^0.5=+-(cos60°+jsin60°)=+-(1+j√3)/2x2=+-(cos240°+jsin240°)^0.5=+-(cos120°+jsin120°)=+-(-1+j√3)/2


2.求x^5+x^4+x^3+x^2+x+1=0所圍成五邊形之面積0=x^6-1=(x-1)(x^5+x^4+x^3+x^2+x+1)x^6=1=cos360°+jsin360°x=(cos360°+jsin360°)^(1/6)x1=cos60°+jsin60°.....戴美弗定理x2=cos120°+jsin120°x3=cos180°+jsin180°x4=cos240°+jsin240°x5=cos300°+jsin300°此5邊形: 每兩者夾角=60°,每邊長=1只有x1,x5的夾角=120°所以面積為:A=4pc*0.5*1*1*sin60°+0.5*1*1*sin120°=2*√3/2+0.5*√3/2=√3+√3/4=5√3/4.....ans

1.參考不知對否
(x^2)^2+(x^2)+1=0
==>x^2=(-1+-i√3)/2
==>x^2=(cos120度+isin120度) 或x^2=(cos240度+isin240度)
==>x=+-(cos120度+isin120度)^(1/2)或x=+-(cos240度+isin240度)^(1/2)
==>x=cos60度+isin60度 ,x=-cos60度-isin60度
x=cos120度+isin120度, x=-cos120度-isin120度