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Home » Similarly, for \( z^3 = \omega^2 = e^-2\pi i/3 \): - 500apps

Similarly, for \( z^3 = \omega^2 = e^-2\pi i/3 \): - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 b_2 = F(b_1) = F(1) = 1 - rac{1^2}{2} = 1 - rac{1}{2} = rac{1}{2}

📌 b_3 = F(b_2) = F\left(rac{1}{2}

📌 ight) = rac{1}{2} - rac{1}{2} \left(rac{1}{2}

📌 ight)^2 = rac{1}{2} - rac{1}{2} \cdot rac{1}{4} = rac{1}{2} - rac{1}{8} = rac{3}{8}

📌 b_4 = F\left(rac{3}{8}

📌 ight) = rac{3}{8} - rac{1}{2} \left(rac{3}{8}

📌 ight)^2 = rac{3}{8} - rac{1}{2} \cdot rac{9}{64} = rac{3}{8} - rac{9}{128} = rac{48 - 9}{128} = rac{39}{128}

📌 b_5 = F\left(rac{39}{128}

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\end{vmatrix} = \mathbf{i}(y \cdot 3 - z \cdot 2) - \mathbf{j}(x \cdot...
= egin{pmatrix} 3y - 2z \ - (3x - z) \ 2x - y \end{pmatrix} = egin{p...
Set equal to \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\):
3y - 2z = 0 \
-3x + z = 0 \
2x - y = 5
From second equation: \(z = 3x\)
From first: \(3y = 2z = 2(3x) = 6x \Rightarrow y = 2x\)
Substitute into third:
2x - (2x) = 5 \Rightarrow 0 = 5

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