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Finding the roots of a polynomial is one of the oldest and most central problems in Algebra. Once the coefficients are allowed to move through the complex plane, the roots start revealing a much richer geometry.Here is the Mathematics, try it yourself and play around with the coefficients and polynomial structure:P(x) = x¹² + a x⁸ + b x⁶ + c x⁴ + d x + 1a = (sin(t₁) + i cos(sin(t₂) + 0.5 sin(2t₂))) Mb = 0.3 (t₁ + t₂) Mᶜc = (exp(i t₁) - cos(t₂)) Md = (cos(t₁) - 0.5 i sin(sin(t₂) + 0.5 sin(2t₂)))
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Finding the roots of a polynomial is one of the oldest and most central problems in Algebra. Once the coefficients are allowed to move through the complex plane, the roots start revealing a much richer geometry.Here is the Mathematics, try it yourself and play around with the coefficients and polynomial structure:P(x) = x¹² + a x⁸ + b x⁶ + c x⁴ + d x + 1a = (sin(t₁) + i cos(sin(t₂) + 0.5 sin(2t₂))) Mb = 0.3 (t₁ + t₂) Mᶜc = (exp(i t₁) - cos(t₂)) Md = (cos(t₁) - 0.5 i sin(sin(t₂) + 0.5 sin(2t₂)))
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