> I obtain the result in the wanted forme....
> How can I test that is it equivalent, this one with the image?
The simplest technique is to evaluate the two expressions for different
values of the parameters, to see if they are the same. In your case,
[maxima_answer, kk_answer],a=1,b=1,c=1,d=1,s=1,omega=%pi/2,rectform
=> [ 2*%I/5+1/5, %I/3 ]
Maxima's answer also appears to be correct. So I suggest you check your
answer.
> And how can I simplify?
There are many techniques for putting expressions in different forms.
The simplest to start with are Ratsimp, Radcan, Factor, Factorsum.
These may or may not 'simplify' in any given case. For example, which
is simpler,
x^2-1 or (x-1) (x+1) ?
How about
(x^100-1)/(x-1) or x^99+x^98+...1 ?
-s