The complex octagon is calculated for complex solutions of polynomials. Using the Perrin polynomial that generates the sequence it is shown that the complex solution can be expressed as a phase vector or phasor. Phasors are used by electrical engineers and physicists in describing current and power in electrical circuits. In a similar manner, the complex phasor describes an ellipse in which the phase represents complex numbers that are roots of other polynomials. These polynomials all factor into the discriminant (-23) of the Perrin polynomial. The phasors can be added and multiplied like electrical components to design other polynomials containing information similar to Perrin’s polynomial. The periodicity of the phase vector for each root of a polynomial suggests that a Fourier Transform on the phasors can provide information about the integer sequence.
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Perrin Sequences My Chalkboard 