Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.3 Tangent Planes and Linear Approximations, #38 · Multivariable Calculus · Partial derivatives

The complex equation … contains two real equations, … from the real…

The complex equation $(x + i y)^{3} = 1$ contains two real equations, $x^{3} - 3 x y^{2} = 1$ from the real part and $3 x^{2} y - y^{3} = 0$ from the imaginary part. Search by computer for the basins of attraction of the three solutions $(1, 0), (- 1/2, 3 /2),$ and $(- 1/2, - 3 /2)$ —which give the cube roots of 1.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.3 Tangent Planes and Linear Approximations, #38

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