Visualization of the Newton's method when computing the roots of Z_____AnTi_QuOtE__QuOtE_____^4=1 (Visualisation de la methode de Newton lors du calcul des racines de Z_____AnTi_QuOtE__QuOtE_____^4=1) {a chapter of 'Mathematics - A Virtual Instrument For Exploring Space Time And Beyond'}

Visualization of the Newton's method when computing the roots of Z⁴=1 [Visualisation de la méthode de Newton lors du calcul des racines de Z⁴=1].

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

[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:

Computation of the roots of Z^2=1 using Newton's method

Z²=1

Computation of the roots of Z^3=1 using Newton's method

Z³=1

Computation of the roots of Z^4=1 using Newton's method

Z⁴=1

Computation of the roots of Z^5=1 using Newton's method

Z⁵=1

Computation of the roots of Z^6=1 using Newton's method

Z⁶=1

Computation of the roots of Z^7=1 using Newton's method

Z⁷=1

Computation of the roots of Z^8=1 using Newton's method

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-:

Visualization of the Newton's method when computing the roots of Z^2=1