[solved]-Using Python Consider Complex Polynomial 3 1z3 1 Whose Zeros Three Cube Roots Unity Genera Q39012547

using python:

Consider the complex polynomial 3−1z3−1, whose zeros are thethree cube roots of unity. Generate a picture showing three basinsof attraction in the complex plane in the square region defined by−1≤Real( )≤1−1≤Real(z)≤1 and −1≤Imaginary( )≤1−1≤Imaginary(z)≤1. Todo this, use a mesh of 1000×10001000×1000 pixels inside the square.The center point of each pixel is used to start the iteration ofNewton’s method. Assign a particular basin color to each pixel ifconvergence to a root is obtained with nmax =10=10iterations. Thecriterion for convergence is to check both| +1− |< |zn+1−zn|<ϵ and | 3 +1−1|< |zn+13−1|<ϵwith asmall value such as =10−4ϵ=10−4 as well as a maximum number ofiterations. First debug your program and get a crude picture withonly a small number of pixels such as 10×1010×10.

You may need to use some Python functions, such asnumpy.meshgrid, matplotlib.pyplot.pcolor.

The grading of this problem will be based on the documentationof your work (your explanation in words and math), the correctnessof the code, and the graphs you show.

Expert Answer

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Answer to using python: Consider the complex polynomial 3−1z3−1, whose zeros are the three cube roots of unity. Generate a… . . .