Try the deusexmachina.mac package. Works wonders.
-s
On Wed, Oct 2, 2013 at 6:47 AM, Jaime Villate <villate at fe.up.pt> wrote:
> Sure, but the question is:
> is there a simple process to realize that sin(atan(37/55)/3)=1/sqrt(26)
> and cos(atan(37/55)/3)=5/sqrt(26)?
> Can that process be implemented in Maxima?
>
> Cheers,
> Jaime
>
>
> On 02-10-2013 10:13, Aleksas Domarkas wrote:
>
>> Example. Find all three cube roots of the complex number 110+74i.
>>
>> (%i1) eq:z^3=polarform(74*%i+110);
>> (%o1) z^3=26^(3/2)*%e^(%i*atan(37/**55))
>> (%i2) T1:sin(atan(37/55)/3)=1/sqrt(**26)$
>> (%i3) T2:cos(atan(37/55)/3)=5/sqrt(**26)$
>> (%i4) solve(eq,z);
>> (%o4)
>> [z=((sqrt(3)*sqrt(26)*%i-sqrt(**26))*%e^((%i*atan(37/55))/3))/**2,
>> z=-((sqrt(3)*sqrt(26)*%i+sqrt(**26))*%e^((%i*atan(37/55))/3))/**2,
>> z=sqrt(26)*%e^((%i*atan(37/55)**)/3)]
>> (%i5) rectform(%)$
>> (%i6) subst([T1,T2],%),radcan,**rectform;
>> (%o6) [z=((5*sqrt(3)-1)*%i)/2+(-**sqrt(3)-5)/2,z=-((5*sqrt(3)+1)**
>> *%i)/2-(5-sqrt(3))/2,z=%i+5]
>> best
>> Aleksas D
>>
>>
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