[Maxima-discuss] Simplification of a trigonometric or exponentialized term

[Roland S. <sal...@gm...>]

The following term I don't manage to simplify, neither in trigonometric nor in exponentialized form nor with ntrig:

 

a:(-1-cos(4*%pi/5)+%i*sin(4*%pi/5))/(1-cos(4*%pi/5)+%i*sin(4*%pi/5));

rectform(a);

float(%);

 

By exponentialization I get

b:exponentialize(a);

radcan(b);

 

I'm pretty sure the term is identical with

c:sqrt(5-2*sqrt(5))*%i/sqrt(5);

float(c);

 

Using load(ntrig); gives from a:

a:(-1-cos(4*%pi/5)+%i*sin(4*%pi/5))/(1-cos(4*%pi/5)+%i*sin(4*%pi/5));

rectform(%);

radcan(%);   

->   d:(sqrt(sqrt(5)+5)*(sqrt(2)*sqrt(5)-sqrt(2))*%i)/(2*sqrt(5)+10);

which again I cannot simplify to c.

 

How can simplification  a ->  c  or b -> c  or  d -> c  be achieved? A wxmx file is annexed.

 

Thanks for any help. Best regards,  

Roland