x^n = 1 の解x=1^(1/x)を1のn乗根という。

n=1		n乗根
x=1 x^2=1 x^3=1 x^4=1 x^5=1	(x+1)(x-1)=0 (x-1)(x^2+x+1)=0 (x-1)(x+1)(x^2+1)=0 (x-1){(x+(1/x))^2+x+(1/x)-1}=0	1 1,-1 1, (-1+i√3)/2, (-1-i √3)/2 1,-1, i, -i 1, (-1/4)[1+(√5)±i (√2)√{5-√5}], (-1/4)[1-(√5)±i (√2)√{5+√5}]
x^6=1	(x-1)(x+1)(x^2+x+1)(x^2-x+1)=0	1,-1, (1±i √3)/2, -(1±i √3)/2
x^7=1	(x-1)[{x+(1/x)}^3+{x+(1/x)}^2-2{x+(1/x)}-1=0	1,-cos(π/7)±i sin(π/7), cos(2π/7)±i sin(2π/7), -cos(3π/7)±i sin(3π/7)
x^7=1		1, (1/12)[(28+ i 84√3)^(-1/3)]*[{(28+ i 84√3)^(2/3)}-2{(28+ i 84√3)^(1/3)}+28±√{672-i 336(√3)+(28+ i 84√3)^(4/3)+84(28+ i 84√3)^(2/3)-112(28+ i 84√3)^(1/3)}], (-1/24)[(28+ i 84√3)^(-1/3)]*[(1-i √3){(28+ i 84√3)^(2/3)}+4{(28+ i 84√3)^(1/3)}+28(1+i √3)±√{672+i 2016(√3)-2(1+i √3)(28+ i 84√3)^(4/3)-336(28+ i 84√3)^(2/3)-224(1+i √3)(28+ i 84√3)^(1/3)}], (-1/24)[(28+ i 84√3)^(-1/3)]*[(1+i √3){(28+ i 84√3)^(2/3)}+4{(28+ i 84√3)^(1/3)}+28(1-i √3)±√{-3360-i 672(√3)-2(1-i √3)(28+ i 84√3)^(4/3)-336(28+ i 84√3)^(2/3)+224(1-i √3)(28+ i 84√3)^(1/3)}],
x^8=1	(x-1)(x+1)(x^2+1)(x^2+√2x+1)(x^2-√2x+1=0	1, -1, i, -i, (1±i)/√2, -(1±i)/√2

x^n=-1

x^n= i

x^n= -i