Beware of the freezing monster WARNING: We will be using large amounts of memory. This may cause some "freezing". When the computer seems to be frozen, restart the computer may help, but try to avoid this by starting with small number of steps and small grids, and increasing slowly. Websites. We continue studying Newton's method Now, let us consider the function f(x)=x^3-1 with domain the complex numbers. EXERCISE: Define a procedure to help you find the roots of f by the Netwon's method. f:=x->x^3-1; 1 is one of the roots of f. Since we are working in the complex domain, there are two more roots. Let's try to find them QUESTION: Is it possible to find all the roots of f by the Newton's method. Why? N:=x->x-f(x)/D(f)(x); newton(-0.45+0.86*I); EXERCISE: Find all the roots of the above map f. Denote one of them as r1, another as r2 and the third one as r3 in any order you want. Define a procedure that takes as an input a complex number z, computes 50 iterates of z by Newton's method, and returns 0.1 if the result is close to r1, 0.2 if it is close to r2 and 0.3 if it is close to r3.