I am trying to calculate a symbolic complex sequence given in the below picture: 

I have written the following code; however, it is not efficient at all and it takes a very long time to calculate even the first elements of the sequences. Can anyone please help me fix that or suggest an efficient way of doing such calculation in complex domain? Any help is appreciated. Thanks

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d(0):=1+1I;

M(0):=1-2I;

for k from 0 to 3 do u(k):=-d(k)/M(k);p(k+1):=M__s*u(k)+d__s;d(k+1):=d(k)+gamma*p(k+1)/(nu+abs(u(k))^2);M(k+1):=M(k)+gamma*p(k+1)*conjugate(u(k))/(nu+abs(u(k))^2);od;

Is there a way to specify different colors for different output variables? For example, if x,y, and z appear in the entire document as variables, I want x to be red, y to be blue, and z to be green whenever an output is displayed.

Thanks

Suppose that I have an expression of the form  eq:=a*x^2+b*y^2+c*x*y, where x,y are real numbers, a>0, b<0, and c>0. Is there a relatively simple way to separate the positive, negative, and indeterminate terms from such an expression. In other words, I want to get  

eq_positive=a*x^2,

 eq_negative=b*y^2,

eq_indeterminate=c*x*y.

Thanks

In the below calculations, I get some solutions after solving the system. I am not sure if this is done assuming that all the values that are under the radicals are positive or indeed they are positive without further assumptions. I mean can I be sure that each given set of solution is a feasible solution? I suspect that Maple may ignore the assumptions sometimes.  

Suppose Delta:=f(a,b)x^2+g(a,b)x+h(a,b), where f,g,h are functions of a and b. Is there a way to find conditions on a,b such that Delta is positive?