Complexity\' the equation z^2 + 1 = 0. i.e., reformulate it as a system f = 0 wh

Question

Complexity' the equation z^2 + 1 = 0. i.e., reformulate it as a system f = 0 where f : IR^2 rightarrow IR^2, and write a MATLAB function imaginaryUnits.m of the form that implements Newton's method for this bivariate problem starting with an initial input Z_0 = x_0 + iy_0. In your commentary, discuss what stopping criterion you are using and why. If any starting values don't lead to convergence, then the limit returned should be NaN. Use the MATLAB function makePlot.m to generate a phase portrait of Problem 2 by running your imaginaryUnits.m function starting from 1000 uniformly spaced initial points from the disk |z| lessthanorequalto 10; color-code the initial points according to whether Newton's method converges to i, converges to -i, or diverges.

Explanation / Answer

The product code C is the code obtained by the following three-step encoding method. In n k the first step, k1 independent information bits are placed in each of k2 rows, thus creating a k2 × k1 rectangular array (see Figure 1a). In the second step, the k1 information bits in each of these k2 rows are encoded into a codeword of length n1 in C1, thus creating a 2 × n1 rectangular array (see Figure 1b). In the third step, the k2 information bits in each of the n1 columns are

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