AVirtualMachineForExploringSpaceTimeAndBeyond : Computation of the roots of Z_____AnTi_QuOtE__QuOtE_____MiseEnExposant(8)=1 using Newton's method (Calcul des racines de Z_____AnTi_QuOtE__QuOtE_____MiseEnExposant(8)=1 grace a la methode de Newton).

Computation of the roots of Z⁸=1 using Newton's method [Calcul des racines de Z⁸=1 grâce à la méthode de Newton].

The eight black squares display the eight complex roots Z=cos(2.k.pi/8)+i*sin(2.k.pi/8) for k={0 -middle right-,1,2,3,4,5,6,7}.

[Plus d'informations à propos de la Méthode de Newton -en français/in french-]

See some related pictures (possibly including this one) displaying the computation of the roots of Zⁿ=1 using Newton's method:

Z²=1

Z³=1

Z⁴=1

Z⁵=1

Z⁶=1

Z⁷=1

Z⁸=1

See some related pictures (possibly including this one) displaying the Newton's method when computing the roots of Zⁿ=1 -sixteen trajectories are exhibibited, their starting points being the big circular dots-: