[newbie] problem with determining modulus of complex quantity
Subject: [newbie] problem with determining modulus of complex quantity
From: Leo Butler
Date: Thu, 21 Nov 2013 15:42:52 GMT
> Date: Thu, 21 Nov 2013 15:58:12 +0100
> From: Hugo Coolens <hugo.coolens at kuleuven.be>
>
> I defined the following function:
> calpgon(m,s):=product(1/(s+4*(cos((k*%pi)/(2*m+1)))^2),k,1,m);
>
> simplified it for the case m=3 like this:
> trigrat(calpgon(3,s));
> 1
> (%o2) -------------------
> 3 2
> s + 5 s + 6 s + 1
>
>
> substituted s by i*omega like this
>
> s : %i*omega;
>
> tried to calculate the modulus of calpgon(3,i*omega) like this
> abs(trigrat(calpgon(3,s)));
>
> and got this:
> ! 3 2 !
> !%i (omega - 6 omega) - 5 omega + 1!
> (%o4) --------------------------------------
> 6 4 2
> omega + 13 omega + 26 omega + 1
>
> however I hoped to get this "neater" form:
> 1
> --------------------------------
> sqrt(omega^6+13 omega^4 +26 omega^2+1)
>
> Can anyone here tell me how to make maxima go for the last expression?
(%i1) calpgon(m,s):=product(1/(s+4*(cos((k*%pi)/(2*m+1)))^2),k,1,m)$
(%i2) trigrat(calpgon(3,%i*?));
(%o2) (%i*(?^3-6*?)-5*?^2+1)/(?^6+13*?^4+26*?^2+1)
(%i3) ratsimp(cabs(%));
(%o3) 1/sqrt(?^6+13*?^4+26*?^2+1)
Leo