Investigate the behavior of Newton’s method for finding complex roots of polynomials with real coefficients. For example, the polynomial p(x) = x2 + 1 has the complex conjugate pair of roots ±i and Newton’s method is xn+1 = 1/ 2 (xn − 1/xn). First, program this method using real arithmetic and real numbers as starting values. Second, modify the program using complex arithmetic but still using only real starting values. Finally, use complex numbers as starting values. Observe the behavior of the iterates in each case.
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