z³=1

Per Euler's formula this is equal to:

$(r⋅e^{i⋅φ})^3=1⋅e^{i⋅2⋅π⋅k},k∈\field{N+}$

$(e^{i⋅φ})^3=e^{i⋅2⋅π⋅k}$

$e^{3⋅i⋅φ}=e^{i⋅2⋅π⋅k}$

$φ_2=÷{2⋅π}{3}⋅1$

$φ_3=÷{2⋅π}{3}⋅2$

$z_2=e^÷{i⋅2⋅π}{3}$

$z_3=e^÷{i⋅2⋅2⋅π}{3}$

Or in traditional coordinates:

$z_2=e^÷{i⋅2⋅π}{3}=\cos ÷{2⋅π}{3}+i⋅\sin ÷{2⋅π}{3}$

$z_3=e^÷{i⋅2⋅2⋅π}{3}=\cos ÷{4⋅π}{3}+i⋅\sin ÷{4⋅π}{3}$

$z_2=-0.5+i⋅÷{√3}{2}$

$z_3=-0.5-i⋅÷{√3}{2}$

Author: Danny (remove the ".nospam" to send)

Last modification on: Sat, 04 May 2024 .