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Polynomial lemniscate

In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n. For any such polynomial p and positive real number c, we may define a set of complex numbers by |p(z)|=c.{\displaystyle |p(z)|=c.} This set of numbers may be equated to points in the real Cartesian plane, leading to an algebraic curve ƒ(x, y) = c of degree 2n, which results from expanding out p(z)p¯(z¯){\displaystyle p(z){\bar {p}}({\bar {z}})} in terms of z = x + iy.

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